On pointwise estimates for maximal and singular integral operators

• Autorzy: A. K. Lerner
• Języki publikacji: EN

Abstrakty

EN

We prove two pointwise estimates relating some classical maximal and singular integral operators. In particular, these estimates imply well-known rearrangement inequalities, $L^p_ω$ and BLO-norm inequalities

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 138
• Numer: 3
• Strony: 285-291

Daty

wydano

2000

otrzymano

1999-09-01

Twórcy

autor

A. K. Lerner

• Odessa

Bibliografia

• [1] R. J. Bagby and D. S. Kurtz, Covering lemmas and the sharp function, Proc. Amer. Math. Soc. 93 (1985), 291-296.
• [2] R. J. Bagby and D. S. Kurtz, A rearranged good λ inequality, Trans. Amer. Math. Soc. 293 (1986), 71-81.
• [3] C. Bennett, Another characterization of BLO, Proc. Amer. Math. Soc. 85 (1982), 552-556.
• [4] C. Bennett, R. DeVore and R. Sharpley, Weak-$L^∞$ and BMO, Ann. of Math. 113 (1981), 601-611.
• [5] C. Bennett and R. Sharpley, Weak-type inequalities for $H^p$ and BMO, in: Proc. Sympos. Pure Math. 35, Amer. Math. Soc., 1979, 201-229.
• [6] K. M. Chong and N. M. Rice, Equimeasurable Rearrangements of Functions, Queen's Papers in Pure and Appl. Math. 28, Queen's University, Kingston, Ont., 1971.
• [7] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 15 (1974), 241-250.
• [8] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254.
• [9] A. Córdoba and C. Fefferman, A weighted norm inequality for singular integrals, Studia Math. 57 (1976), 97-101.
• [10] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
• [11] B. Jawerth and A. Torchinsky, Local sharp maximal functions, J. Approx. Theory 43 (1985), 231-270.
• [12] F. John, Quasi-isometric mappings, in: Seminari 1962-1963 di Analisi, Algebra, Geometria e Topologia (Roma, 1964), Ediz. Cremonese, Roma, 1965, 462-473.
• [13] M. A. Leckband, Structure results on the maximal Hilbert transform and two-weight norm inequalities, Indiana Univ. Math. J. 34 (1985), 259-275.
• [15] A. K. Lerner, On weighted estimates of non-increasing rearrangements, East J. Approx. 4 (1998), 277-290.
• [16] S. Spanne, Sur l'interpolation entre les espaces $L_k^pΦ$, Ann. Scuola Norm. Sup. Pisa 20 (1966), 625-648.
• [17] E. M. Stein, Singular integrals, harmonic functions, and differentiability properties of functions of several variables, in: Proc. Sympos. Pure Math. 10, Amer. Math. Soc., 1967, 316-335.
• [18] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
• [19] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.
• [20] J.-O. Strömberg, Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J. 28 (1979), 511-544.