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Amalgams of $L^p$ and $l^q$
Author(s):
John J. F.
Fournier;
James
Stewart
Journal:
Bull. Amer. Math. Soc.
13
(1985),
1-21.
MSC (1980):
Primary 01A60, 42-02, 42-03, 43-02, 43A05, 43A15, 43A25, 46E30;
Secondary 41A05, 41A15, 42A55, 42A75, 42B30, 43A20, 47B10, 47G05
MathSciNet review:
788385
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References:
- [AH] N. E. Aguilera and E. O. Harboure, On the search for weighted norm inequalities for the Fourier transform, Pacific J. Math. 104 (1983), 1-14. MR 683723
- [AI] A. B. Aleksandrov, Majorization property for multidimensional Hardy-Stein-Weiss classes, Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 3 (1982), 97-98. (Russian) MR 672602
- [AG1] L. Argabright and J. Gil de Lamadrid, Fourier analysis of unbounded measures on locally compact abelian groups, Mem. Amer. Math. Soc. 145 (1974). MR 621876
- [AG2] L. Argabright and J. Gil de Lamadrid, AImost periodic measures (preprint).
- [AS] N. Aronszajn and P. Szeptycki, On general integral transformations, Math. Ann. 163 (1966), 127-154. MR 190799
- [BaS] A. Baernstein and E. T. Sawyer, Embedding and multiplier theorems for H (R) (preprint).
- [BP] A. Benedek and R. Panzone, The spaces L, Duke Math. J. 28 (1961), 301-324. MR 126155
- [BF] C. Berg and G. Forst, Potential theory on locally compact abelian groups, Springer-Verlag, 1975. MR 481057
- [Ber1] J.-P. Bertrandias, Sur les théorèmes de Littlewood et d'Orlicz-Paley-Sidon, Groupe de travail d'Analyse Harmonique Grenoble II (1984), III.1-III.9.
- [Ber2] J.-P. Bertrandias, Espaces lp(lα), Groupe de travail d'Analyse Harmonique Grenoble II (1984), IV.l-IV.11.
- [BDD] J.-P. Bertrandias, C. Datry and C. Dupuis, Unions et intersections d'espaces L, Ann. Inst. Fourier (Grenoble) 28 (1978), 53-84. MR 499586
- [BD] J.-P. Bertrandias and C. Dupuis, Transformation de Fourier sur les espaces $l\spp(L\sp{p\sp{\prime} })$, Ann. Inst. Fourier (Grenoble) 29 (1979), 189-206. MR 526784
- [Bes] A. S. Besicovitch, Almost periodic functions, Cambridge Univ. Press, 1932.
- [BiS] M. S. Birman and M. Z. Solomjak, On estimates of singular numbers of integral operators. III: Operators on unbounded domains, Vestnik Leningrad Univ. 24 (1960), 35-48; English transl. in Vestnik Leningrad Univ. Math. 2 (1975), 9-27. MR 246163
- [Bo] H. Bohr, Zur Theorie der fast periodischen Funktionen. I: Eine Verallgameinerung der Fourierreichen, Acta Math. 45 (1924), 29-127. MR 1555192
- [Br] H. Bruhat, Distributions sur un groupe localement compact et applications a l'étude des representations des groupes p-adiques, Bull. Soc. Math. France 89 (1961), 43-75. MR 140941
- [Bur1] R. Bürger, Functions of translation type and Wiener's algebra, Arch. Math. (Basel) 36 (1981), 73-78. MR 612239
- [Bur2] R. Bürger, Functions of translation type and solid Banach spaces of functions, Pacific J. Math. 100 (1982), 259-269. MR 669326
- [BuS] R. C. Busby and H. A. Smith, Product-convolution operators and mixed-norm spaces, Trans. Amer. Math. Soc. 263 (1981), 309-341. MR 594411
- [Cac] N. P. Các, Sur une classe d'espaces de fonctions continues, C. R. Acad. Sci. Paris Sér. A 267 (1968), 775-778. MR 241961
- [Cav] D. J. Caveny, Absolute convergence factors for H, Canad. J. Math. 21 (1969), 187-195. MR 257371
- [CFR] A. Cooper, J. Feldman and L. Rosen, Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework, Ann. Physics 137 (1981), 213-261. MR 640319
- [Coop] J. L. B. Cooper, Positive definite functions of a real variable, Proc. London Math. Soc. (3) 10 (1960), 53-66. MR 116186
- [Cow] M. Cowling, Some applications of Grothendieck's theory of topological tensor products in harmonic analysis, Math. Ann. 232 (1978), 273-285. MR 493165
- [Da] M. M. Day, Some more uniformly convex spaces, Bull. Amer. Math. Soc. 47 (1941), 504-507. MR 4068
- [DKK] K. de Leeuw, J. P. Kahane and Y. Katznelson, Sur les coefficients de Fourier des fonctions continues, C. R. Acad. Sci. Paris Sér. A 285 (1977), 1001-1003. MR 510870
- [Du] C. Dupuis, Un exemple d'utilisation du théorème d'Orlicz-Paley-Sidon, Groupe de travail d'Analyse Harmonique Grenoble I (1981/82), VI.1-VI.3.
- [Eb] W. F. Eberlein, Characterizations of Fourier-Stieltjes transforms, Duke Math. J. 22 (1955), 465-468. MR 72424
- [Ed] R. E. Edwards, Changing signs of Fourier coefficients, Pacific J. Math. 15 (1965), 463-475. MR 200676
- [EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and multiplier theory, Springer-Verlag, 1977. MR 618663
- [EH] R. E. Edwards and H. Helson, Absolute Fourier multipliers, Resultate Math. 4 (1982), 22-33. MR 625111
- [EHR] R. E. Edwards, E. Hewitt and G. Ritter, Fourier multipliers for certain spaces of functions with compact supports, Invent. Math. 40 (1977), 37-57. MR 435739
- [Fei1] H. G. Feichtinger, A characterization of Wiener's algebra on locally compact groups, Arch. Math. (Basel) 29 (1977), 136-140. MR 467170
- [Fei2] H. G. Feichtinger, Un espace de distributions tempérées sur les groupes localement compactes abéliens, C. R. Acad. Sci. Paris Sér A 290 (1980), no. 17, 791-794. MR 580567
- [Fei3] H. G. Feichtinger, Banach convolution algebras of Wiener's type (Proc. Conf. Functions, Series, Operators, Budapest, 1980), Colloq. Math. Soc. János Bolyai, North-Holland, 1983. MR 751019
- [Fei4] H. G. Feichtinger, Banach spaces of distribution of Wiener's type and interpolation (Proc. Conf., Oberwolfach, 1980), Functional Analysis and Approximation (P. Butzer, B. Sz.-Nagy and E. Gorlich, eds.), Birkhaüser-Verlag, 1981, pp. 153-165. MR 650272
- [Fei5] H. G. Feichtinger, Strong almost peridocity and Wiener type spaces, Proc. Conf. Constructive Function Theory (Varna, 1981) (to appear). MR 729887
- [FG] H. Feichtinger and P. Gröbner, Banach spaces of distributions defined by decomposition methods (preprint). MR 910054
- [Fou1] J. J. F. Fournier, On the Hausdorff-Young theorem for amalgams, Monatsh. Math. 95 (1983), 117-135. MR 697152
- [Fou2] J. J. F. Fournier, Lacunarity for amalgams (preprint). MR 892458
- [Ga] E. Gagliardo, On integral transformations with positive kernel, Proc. Amer. Math. Soc. 16 (1965), 429-434. MR 177314
- [Gau] G. I. Gaudry, Quasimeasures and operators commuting with convolution, Pacific J. Math. 18 (1966), 461-476. MR 203502
- [GdL] J. Gil de Lamadrid, Review of [Stw2], Math. Rev. 81i:43001.
- [Go] R. R. Goldberg, On a space of functions of Wiener, Duke Math. J. 34 (1967), 683-691. MR 217614
- [Haj] D. Hajela, Construction techniques for some thin sets in duals of compact abelian groups, Thesis, Ohio State Univ., 1983.
- [Hed] J. H. Hedlund, Multipliers of H, J. Math. Mech. 18 (1968/69), 1067-1074. MR 243080
- [Her] C. S. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms, J. Math. Mech. 18 (1968), 283-323. MR 438109
- [H1] F. Holland, Harmonic analysis on amalgams of L, J. London Math. Soc. (2) 10 (1975), 295-305. MR 374817
- [H2] F. Holland, On the representation of functions as Fourier transforms of unbounded measures, Proc. London Math. Soc. (3) 30 (1975), 347-365. MR 397295
- [Hu] R. A. Hunt, On L(p, q) spaces, Enseign. Math. (2) 12 (1966), 249-276. MR 223874
- [JR] A. Jakimovski and D. C. Russell, Interpolation by functions with mth derivative in pre-assigned spaces, Approximation Theory III (E. W. Cheney, ed.), Academic Press, New York, 1980, pp. 531-536. MR 602764
- [Jo] R. Johnson, Lipschitz spaces, Littlewood-Paley spaces and convoluteurs, Proc. London Math. Soc. (3) 29 (1974), 127-141. MR 355578
- [Ka] S. Karlin, Positive operators, J. Math. Mech. 8 (1959), 907-937. MR 114138
- [Ke] C. N. Kellogg, An extension of the Hausdorff-Young theorem, Michigan Math. J. 18 (1971), 121-127. MR 280995
- [Kh] S. V. Khrushchev, Paley singularities of power series, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 30 (1972), 176-178, English transl, in J. Soviet Math. 4 (1975), 456-459. MR 340562
- [K] G. Köthe, Topological vector spaces. I, Springer-Verlag, 1969. MR 248498
- [La] R. Latter, A characterization of Hp (Rn) in terms of atoms, Studia Math. 62 (1978), 93-101. MR 482111
- [Lin] V. Ja. Lin, On equivalent norms in the space of square summable entire functions of exponential type, Mat. Sb. 67(109) (1965), 586-608; English transl, in Amer. Math. Soc. Transl. (2) 79 (1969), 53-76. MR 187074
- [LVW] T.-S. Liu, A. van Rooij and J.-K. Wang, On some group algebra; modules related to Wiener's algebra M, Pacific J. Math. 55 (1974), 507-520. MR 370060
- [LR] J. M. López and K. A. Ross, Sidon sets, Dekker, New York, 1975. MR 440298
- [M] G. Muraz, Transformation de Fourier et espaces solides, Groupe de travail d'analyse harmonique Grenoble (1984), II.1-II.12.
- [Or] W. Orlicz, Beitrage zur Theorie der Orthogonalentwicklungen (III), Bull. Acad. Polon. Sci. 8/9 (1932), 229-238.
- [P] R. E. A. C. Paley, A note on power series, J. London Math. Soc. 7 (1932), 122-130.
- [Rei1] H. Reiter, Subalgebras of L, Nederl. Akad. Wetensch. Proc. Ser. A 68 = Indag. Math. 27 (1965), 697-701. MR 194908
- [Rei2] H. Reiter, Classical harmonic analysis and locally compact groups, Oxford University Press, 1968. MR 306811
- [Rie] M. A. Rieffel, Multipliers and tensor products of L, Studia Math. 33 (1969), 71-82. MR 244764
- [RS] N. M. Riviere and Y. Sagher, On two theorems of Paley, Proc. Amer. Math. Soc. 42 (1974), 238-242. MR 344779
- [Sch] I. J. Schoenberg, Cardinal interpolation and spline functions, J. Approx. Theory 2 (1969), 167-206. MR 257616
- [Seg] I. E. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc. 61 (1947), 69-105. MR 19617
- [Sid] S. Sidon, Ein Satz uber die Fourierschen Reihen stetiger Funktionen, Math. Z. 34 (1932), 485-486. MR 1545268
- [Sim] B. Simon, Trace ideals and their applications, Cambridge Univ. Press, London, 1979. MR 541149
- [SI] W. T. Sledd, Some inequalities related to the Hausdorff-Young theorem, Proc. Amer. Math. Soc. 42 (1974), 535-540. MR 344780
- [SS] W. T. Sledd and D. A. Stegenga, An H, Ark. Mat. 19 (1981), 265-270. MR 650500
- [Stc] S. B. Steckin, An extremal problem for polynomials, Izv. Akad. Nauk SSSR Ser. Mat. 20 (1956), 765-774; English transl, in Amer. Math. Soc. Transl. (2) 14 (1960), 173-180. MR 83572
- [Stn] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, 1970. MR 290095
- [Stp] W. Stepanoff, Uber einige Verallgemeinerungen der fast periodischen Funktionen, Math. Ann. 95 (1926), 473-498. MR 1512290
- [Stw1] J. Stewart, Unbounded positive definite functions, Canad. J. Math. 21 (1969), 1309-1318. MR 251461
- [Stw2] J. Stewart, Fourier transforms of unbounded measures, Canad. J. Math. 31 (1979), 1281-1292. MR 553161
- [SW] J. Stewart and S. Watson, Which amalgams are convolution algebras? Proc. Amer. Math. Soc. 93 (1985), 621-627. MR 776191
- [Sz1] P. Szeptycki, Some remarks on the extended domain of Fourier transform, Bull. Amer. Math. Soc. 73 (1967), 398-402. MR 208277
- [Sz2] P. Szeptycki, Domains of integral transformations on general measure spaces, Math. Ann. 242 (1979), 267-271. MR 545218
- [Sz3] P. Szeptycki, On some problems related to the extended domain of the Fourier transform, Rocky Mountain J. Math. 10 (1980), 99-103. MR 573865
- [TW] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 68-149. MR 604370
- [Th] M. L. Thornett, A class of second-order stationary random measures, Stochastic Process Appl. 8 (1979), 323-334. MR 535307
- [Tr] H. Triebel, Theory of function spaces, Birkhauser-Verlag, Basel-Boston-Stuttgart, 1983. MR 781540
- [W1] N. Wiener, On the representation of functions by trigonometrical integrals, Math. Z. 24 (1926), 575-616. MR 1544780
- [W2] N. Wiener, Tauberian theorems, Ann. of Math. 33 (1932), 1-100.
- [Wil] L. R. Williams, Generalized Hausdorff-Young inequalities and mixed norm spaces, Pacific J. Math. 38 (1971), 823-833. MR 310555
- [Wln] J. M. Wilson, A simple proof of the atomic decomposition of $H\spp( R\spn)$, $0<płeq 1$, Studia Math. 74 (1982), 25-33.
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01A60, 42-02, 42-03, 43-02, 43A05, 43A15, 43A25, 46E30, 41A05, 41A15, 42A55, 42A75, 42B30, 43A20, 47B10, 47G05
Additional Information:
DOI:
10.1090/S0273-0979-1985-15350-9
PII:
S 0273-0979(1985)15350-9
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