Extensions of Hardy spaces and their use in analysis
HTML articles powered by AMS MathViewer
- by Ronald R. Coifman and Guido Weiss PDF
- Bull. Amer. Math. Soc. 83 (1977), 569-645
References
- R. P. Boas Jr., Isomorphism between $H^p$ and $L^p$, Amer. J. Math. 77 (1955), 655–656. MR 77704, DOI 10.2307/2372590
- D. L. Burkholder, R. F. Gundy, and M. L. Silverstein, A maximal function characterization of the class $H^{p}$, Trans. Amer. Math. Soc. 157 (1971), 137–153. MR 274767, DOI 10.1090/S0002-9947-1971-0274767-6 3. A. P. Calderón and A. Torchinsky, Spaces of distributions in L (R) (to appear).
- A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. MR 100768, DOI 10.2307/2372441
- A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 52553, DOI 10.1007/BF02392130
- A.-P. Calderón and A. Zygmund, On higher gradients of harmonic functions, Studia Math. 24 (1964), 211–226. MR 167631, DOI 10.4064/sm-24-2-211-226
- S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 (1963), 175–188 (Italian). MR 156188 8. L. Carleson, Two remarks on H, Analyse Harmonique d’Orsay 164 (1975), 1-11. 9. F. Carlson, Une inégalité, Ark. Mat. Astronom. Fys. 25B, no. 1, (1934), 1-5.
- Ronald R. Coifman, A real variable characterization of $H^{p}$, Studia Math. 51 (1974), 269–274. MR 358318, DOI 10.4064/sm-51-3-269-274
- Ronald R. Coifman, Characterization of Fourier transforms of Hardy spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 4133–4134. MR 394000, DOI 10.1073/pnas.71.10.4133
- Ronald R. Coifman and Miguel de Guzmán, Singular integrals and multipliers on homogeneous spaces, Rev. Un. Mat. Argentina 25 (1970/71), 137–143. MR 320644
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
- R. R. Coifman, R. Rochberg, and Guido Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), no. 3, 611–635. MR 412721, DOI 10.2307/1970954
- R. R. Coifman and Guido Weiss, On subharmonicity inequalities involving solutions of generalized Cauchy-Riemann equations, Studia Math. 36 (1970), 77–83. MR 271382, DOI 10.4064/sm-36-1-77-83
- Ronald R. Coifman and Guido Weiss, Invariant systems of conjugate harmonic functions associated with compact Lie groups, Studia Math. 44 (1972), 301–308. MR 340986, DOI 10.4064/sm-44-4-301-308
- Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948, DOI 10.1007/BFb0058946
- Ronald R. Coifman and Guido Weiss, Théorèmes sur les multiplicateurs de Fourier sur $\textrm {SU}(2)$ et $\sum _{2}$, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A928–A930 (French). MR 271274
- Ronald R. Coifman and Guido Weiss, Multiplier transformations of functions on $\textrm {SU}(2)$ and $\sum _2$, Rev. Un. Mat. Argentina 25 (1970/71), 145–166. MR 320643
- William C. Connett and Alan L. Schwartz, A multiplier theorem for ultraspherical series, Studia Math. 51 (1974), 51–70. MR 358209, DOI 10.4064/sm-51-1-51-70
- Mischa Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105–167 (1956) (English, with Spanish summary). MR 84632
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- P. L. Duren, B. W. Romberg, and A. L. Shields, Linear functionals on $H^{p}$ spaces with $0<p<1$, J. Reine Angew. Math. 238 (1969), 32–60. MR 259579 25. A. Erdélyi et al., Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953. MR 15, 419; 34 #1565.
- E. B. Fabes and N. M. Rivière, Singular integrals with mixed homogeneity, Studia Math. 27 (1966), 19–38. MR 209787, DOI 10.4064/sm-27-1-19-38
- Charles Fefferman, Harmonic analysis and $H^{p}$ spaces, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974) MAA Stud. Math., Vol. 13, Math. Assoc. Amer., Washington, D.C., 1976, pp. 38–75. MR 0461001
- Charles Fefferman, Characterizations of bounded mean oscillation, Bull. Amer. Math. Soc. 77 (1971), 587–588. MR 280994, DOI 10.1090/S0002-9904-1971-12763-5
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
- C. Fefferman, N. M. Rivière, and Y. Sagher, Interpolation between $H^{p}$ spaces: the real method, Trans. Amer. Math. Soc. 191 (1974), 75–81. MR 388072, DOI 10.1090/S0002-9947-1974-0388072-3
- G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403 32. J. Garcia-Cuerva, Weighted H, Ph. D. Thesis, Washington Univ., Missouri, 1975. 33. G. H. Hardy, The mean value of the modules of an analytic function, Proc. London Math. Soc. (2) 14 (1915), 269-277.
- Carl Herz, Bounded mean oscillation and regulated martingales, Trans. Amer. Math. Soc. 193 (1974), 199–215. MR 353447, DOI 10.1090/S0002-9947-1974-0353447-5
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
- Satoru Igari, An extension of the interpolation theorem of Marcinkiewicz. II, Tohoku Math. J. (2) 15 (1963), 343–358. MR 158205, DOI 10.2748/tmj/1178243771
- F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
- B. Frank Jones Jr., A class of singular integrals, Amer. J. Math. 86 (1964), 441–462. MR 161099, DOI 10.2307/2373175
- A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489–578. MR 460543, DOI 10.2307/1970887
- A. W. Knapp and E. M. Stein, Singular integrals and the principal series. I, II, Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 281–284; ibid. 66 (1969), 13–17. MR 263989, DOI 10.1073/pnas.66.1.13
- A. Korányi and S. Vági, Singular integrals on homogeneous spaces and some problems of classical analysis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 25 (1971), 575–648 (1972). MR 463513
- Paul Krée, Distributions quasi homogènes. Généralisations des intégrales singulières et du calcul symbolique de Calderón-Zygmund, C. R. Acad. Sci. Paris 261 (1965), 2560–2563 (French). MR 188779 44. V. Krylov, Functions regular in the half-plane, Sbornik 6 (1939), 95-138. (Russian) 45. R. Macias, H, Ph. D. Thesis, Washington Univ., Missouri, 1975.
- Norman G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717–721. MR 168712, DOI 10.1090/S0002-9939-1964-0168712-3
- B. Muckenhoupt and E. M. Stein, Classical expansions and their relation to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), 17–92. MR 199636, DOI 10.1090/S0002-9947-1965-0199636-9 48. F. Riesz, Sur les valeurs moyennes du module des fonctions harmoniques et des fonctions analytiques, Acta Sci. Math. 1 (1922/23), 27-32.
- N. M. Rivière, Singular integrals and multiplier operators, Ark. Mat. 9 (1971), 243–278. MR 440268, DOI 10.1007/BF02383650
- Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Donald Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391–405. MR 377518, DOI 10.1090/S0002-9947-1975-0377518-3
- E. M. Stein, Note on the class $L$ $\textrm {log}$ $L$, Studia Math. 32 (1969), 305–310. MR 247534, DOI 10.4064/sm-32-3-305-310 54. E. M. Stein, Classes H, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A716-A719, A780-A781; ibid. 264 (1967), A107-A108. MR 37 #695a, b, c.
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- E. M. Stein and Guido Weiss, On the interpolation of analytic families of operators acting on $H^{p}$-spaces, Tohoku Math. J. (2) 9 (1957), 318–339. MR 94704, DOI 10.2748/tmj/1178244785
- Elias M. Stein and Guido Weiss, On the theory of harmonic functions of several variables. I. The theory of $H^{p}$-spaces, Acta Math. 103 (1960), 25–62. MR 121579, DOI 10.1007/BF02546524
- E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163–196. MR 223492, DOI 10.2307/2373431
- M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
- Guido Weiss, Complex methods in harmonic analysis, Amer. Math. Monthly 77 (1970), 465–474. MR 261270, DOI 10.2307/2317379
- Studies in real and complex analysis, Studies in Mathematics, Vol. 3, Mathematical Association of America, Buffalo, N.Y.; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. I. I. Hirschman, Jr., editor. MR 0183600
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- Journal: Bull. Amer. Math. Soc. 83 (1977), 569-645
- MSC (1970): Primary 30A78, 42A18, 42A40; Secondary 32A07, 42A56, 43A85
- DOI: https://doi.org/10.1090/S0002-9904-1977-14325-5
- MathSciNet review: 0447954