Application of a theorem of M. G. KreÄn to singular integrals
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- by Rainer Wittmann PDF
- Trans. Amer. Math. Soc. 299 (1987), 581-599 Request permission
Abstract:
We give Hölder and ${L^2}$ estimates for singular integrals on homogeneous spaces in the sense of Coifman and Weiss. The fundamental tool which allows us to pass from Hölder to ${L^2}$ estimates, is a theorem of M. G. Krein.References
- A. P. CalderĂłn and A. Zygmund, Singular integrals and periodic functions, Studia Math. 14 (1954), 249â271 (1955). MR 69310, DOI 10.4064/sm-14-2-249-271
- Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogĂšnes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Ătude de certaines intĂ©grales singuliĂšres. MR 0499948, DOI 10.1007/BFb0058946
- Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569â645. MR 447954, DOI 10.1090/S0002-9904-1977-14325-5
- Mischa Cotlar, A unified theory of Hilbert transforms and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105â167 (1956) (English, with Spanish summary). MR 84632
- Guy David and Jean-Lin JournĂ©, A boundedness criterion for generalized CalderĂłn-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371â397. MR 763911, DOI 10.2307/2006946
- 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. 95â118. MR 0510853
- Israel Gohberg and Naum Krupnik, EinfĂŒhrung in die Theorie der eindimensionalen singulĂ€ren Integraloperatoren, LehrbĂŒcher und Monographien aus dem Gebiete der Exakten Wissenschaften (LMW). Mathematische Reihe [Textbooks and Monographs in the Exact Sciences. Mathematical Series], vol. 63, BirkhĂ€user Verlag, Basel-Boston, Mass., 1979 (German). Translated from the Russian by B. SchĂŒppel. MR 545507, DOI 10.1007/978-3-0348-5555-6
- A. W. Knapp and E. M. Stein, Intertwining operators for semisimple groups, Ann. of Math. (2) 93 (1971), 489â578. MR 460543, DOI 10.2307/1970887 A. Korn, Ăber MinimalflĂ€chen, deren Randkurven wenig von ebenen Kurven abweichen, Abhandl. Königl. Preuss. Akad. Wiss., Berlin, 1909.
- Roberto A. MacĂas and Carlos Segovia, Lipschitz functions on spaces of homogeneous type, Adv. in Math. 33 (1979), no. 3, 257â270. MR 546295, DOI 10.1016/0001-8708(79)90012-4
- Roberto A. MacĂas and Carlos Segovia, Singular integrals on generalized Lipschitz and Hardy spaces, Studia Math. 65 (1979), no. 1, 55â75. MR 554541, DOI 10.4064/sm-65-1-55-75
- Norman G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717â721. MR 168712, DOI 10.1090/S0002-9939-1964-0168712-3
- Mitchell H. Taibleson, The preservation of Lipschitz spaces under singular integral operators, Studia Math. 24 (1964), 107â111. MR 162133, DOI 10.4064/sm-24-1-107-111
- A. Zygmund, On the preservation of classes of functions, J. Math. Mech. 8 (1959), 889-895; erratum 9 (1959), 663. MR 0117498, DOI 10.1512/iumj.1960.9.59040
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 299 (1987), 581-599
- MSC: Primary 42B20; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869223-X
- MathSciNet review: 869223