Bulletin of the American Mathematical Society

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Book Information:

Author: Alberto Torchinsky
Title: Real variable methods in harmonic analysis
Additional book information: Pure and Applied Mathematics, vol. 123, Academic Press, Inc., Orlando, 1986, xii + 462 pp., $89.00 ($45.00 paper). ISBN 0-12-695460-7.

Authors: J. García-Cuerva and J. L. Rubio de Francia
Title: Weighted norm inequalities and related topics
Additional book information: Mathematical Studies, vol. 116, North-Holland, Amsterdam, New York, Oxford, 1985, x + 604 pp., ISBN 0-444-87804-1.

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

A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324

A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16–36. MR 104925, DOI 10.2307/2372819

A.-P. Calderón, Commutators, singular integrals on Lipschitz curves and applications, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 85–96. MR 562599

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

Sun-Yung A. Chang and Robert Fefferman, Some recent developments in Fourier analysis and $H^p$-theory on product domains, Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 1–43. MR 766959, DOI 10.1090/S0273-0979-1985-15291-7

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 and Miguel de Guzmán, Singular integrals and multipliers on homogeneous spaces, Rev. Un. Mat. Argentina 25 (1970/71), 137–143. MR 320644

Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170

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

Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5

Guy David, Opérateurs de Calderón-Zygmund, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 890–899 (French). MR 934291

Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911, DOI 10.2307/2006946

G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56 (French). MR 850408, DOI 10.4171/RMI/17

Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655

Charles Fefferman, Recent progress in classical Fourier analysis, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 95–118. MR 0510853

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

Michael Frazier and Björn Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777–799. MR 808825, DOI 10.1512/iumj.1985.34.34041

20.

M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces (submitted).

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

Jean-Lin Journé, Calderón-Zygmund operators, pseudodifferential operators and the Cauchy integral of Calderón, Lecture Notes in Mathematics, vol. 994, Springer-Verlag, Berlin, 1983. MR 706075, DOI 10.1007/BFb0061458

J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121

Yves Meyer, Ondelettes et opérateurs. I, Actualités Mathématiques. [Current Mathematical Topics], Hermann, Paris, 1990 (French). Ondelettes. [Wavelets]. MR 1085487

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, Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 173–189. MR 0578903

E. M. Stein (ed.), Beijing lectures in harmonic analysis, Annals of Mathematics Studies, vol. 112, Princeton University Press, Princeton, NJ, 1986. MR 864369

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

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

30.

E. M. Stein, Guido Weiss and Mary Weiss, H, Proc. Nat. Acad. Sci. U.S.A. (1964), 1035-1039.

A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

1.

D. Burkholder, R. Gundy and M. Silverstein, A maximal function characterization of the class H, Trans. Amer. Math. Soc. 157 (1971), 137-153. MR 0274767

2.

A. P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1091-1099. MR 466568

3.

A. P. Calderón, Uniqueness in the Cauchy problem for partial differential equations, Amer. J. Math. 80 (1958), 16-36. MR 104925

4.

A. P. Calderón, Commutators, singular integrals on Lipschitz curves and applications, Internat. Congress Math., Helsinki, 1978, pp. 85-96. MR 562599

5.

A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. MR 52553

6.

A. P. Calderón and A. Zygmund, On higher gradients of harmonic functions, Studia, Math. 24 (1964), 211-226. MR 167631

7.

S.-Y. A. Chang and R. Fefferman, Some recent developments in Fourier analysis on product domains, Bull. Amer. Math. Soc. (NS) 12 (1985), 1-44. MR 766959

8.

R. R. Coifman, A real variable characterization of H, Studia Math. 51 (1974), 269-274. MR 358318

9.

R. R. Coifman and M. de Guzmán, Singular integrals and multipliers on homogeneous spaces, Rev. Un. Mat. Argentina 25 (1970/1971), 137-143. MR 320644

10.

R. R. Coifman and Y. Meyer, Au-delà des opérateurs pseudodifférentiels, Astérisque 57, Soc. Math De France, 1978. MR 518170

11.

R. R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math., vol. 242, Springer-Verlag, Berlin and New York, 1971. MR 499948

12.

R. R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 447954

13.

G. David, Opérateurs de Calderón-Zygmund, Internat. Congress Math., Berkeley, 1986, pp. 890-899. MR 934291

14.

G. David and J.-L. Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), 371-397. MR 763911

15.

G. David, J.-L. Journé and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Ibero-Americana 1 (1985), 1-56. MR 850408

16.

P. L. Duren, Theory of H, Academic Press, New York, 1970. MR 268655

17.

C. Fefferman, Recent progress in classical Fourier analysis, Internat. Congress Math., Vancouver, 1974, pp. 95-118. MR 510853

18.

C. Fefferman and E. M. Stein, H, Acta Math. 129 (1972), 137-193. MR 447953

19.

M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799. MR 808825

20.

M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces (submitted).

21.

F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. MR 131498

22.

J.-L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math., vol. 994, Springer-Verlag, Berlin and New York, 1983. MR 706075

23.

J. J. Kohn and L. Nirenberg, On the algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 176362

24.

Y. Meyer, Ondelettes et opérateurs (to appear). MR 1085487

25.

E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970. MR 290095

26.

E. M. Stein, Some problems in harmonic analysis suggested by symmetric spaces and semi-simple Lie groups, Proc. Internat. Congr. Math., Nice 1 (1970), 173-189. MR 578903

27.

E. M. Stein, Beijing lectures in harmonic analysis, edited by Stein, Ann. of Math. Studies, no. 112, Princeton Univ. Press, Princeton, N. J., 1986. MR 864369

28.

E. M. Stein and Guido Weiss, On the theory of harmonic functions of several variables, Acta Math. 103 (1960), 26-62. MR 121579

29.

E. M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N. J., 1971. MR 304972

30.

E. M. Stein, Guido Weiss and Mary Weiss, H, Proc. Nat. Acad. Sci. U.S.A. (1964), 1035-1039.

31.

A. Zygmund, Trigonometric series, 2nd ed., Cambridge Univ. Press, Cambridge, 1959. MR 107776