QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS

Abstract

References

Metrics

doi:10.1007/s10473-019-0417-x

Abstract: In this article, the authors consider the weighted bounds for the singular integral operator defined by

where Ω is homogeneous of degree zero and has vanishing moment of order one, and A is a function on Rⁿ such that ▽A ∈ BMO(Rⁿ). By sparse domination, the authors obtain some quantitative weighted bounds for T_A when Ω satisfies regularity condition of L^r-Dini type for some r ∈ (1, ∞).

Key words: Singular integral operator, sparse domination, A_p constant, maximal operator

CLC Number:

42B20

Wenhua GAO, Guoen HU. QUANTITATIVE WEIGHTED BOUNDS FOR A CLASS OF SINGULAR INTEGRAL OPERATORS[J].Acta mathematica scientia,Series B, 2019, 39(4): 1149-1162.

Trendmd

[1] Buckley S M. Estimates for operator norms on weighted spaces and reverse Jensen inequalities. Trans Amer Math Soc, 1993, 340:253-272
[2] Cohen J. A sharp estimate for a multilinear singular integral on Rn. Indiana Univ Math J, 1981, 30:693-702
[3] Damián W, Hormozi M, Li K. New bounds for bilinear Calderón-Zygmund operators and applications. arxiv:1512.02400
[4] Grafakos L. Modern Fourier Analysis. GTM 250. 2nd Edition. New York:Springer, 2008
[5] Hofmann S. On certain non-standard Calderón-Zygmund operators. Studia Math, 1994, 109:105-131
[6] Hu G. Weighted vector-valued estimates for a non-standard Calderón-Zygmund operator. Nonlinear Anal, 2017, 165:143-162
[7] Hu G, Li D. A Cotlar type inequality for the multilinear singular integral operators and its applications. J Math Anal Appl, 2004, 290:639-653
[8] Hu G, Yang D. Sharp function estimates and weighted norm inequalities for multilinear singular integral operators. Bull London Math Soc, 2003, 35:759-769
[9] Hytönen T. The sharp weighted bound for general Calderón-Zygmund operators. Ann Math, 2012, 175:1473-1506
[10] Hytönen T, Lacey M, Pérez C. Sharp weighted bounds for the q-variation of singular integrals. Bull London Math Soc, 2013, 45:529-540
[11] Hytönen T, Pérez C. Sharp weighted bounds involving A∞. Anal PDE, 2013, 6:777-818
[12] Hytönen T, Pérez C. The L(log L)^ε endpoint estimate for maximal singular integral operators. J Math Anal Appl, 2015, 428:605-626
[13] Lacey M, Li K. On Ap- A∞ type estimates for square functions. Math Z, 2016, 284:1211-1222
[14] Lerner A K. On pointwise estimate involving sparse operator. New York J Math, 2016, 22:341-349
[15] Lerner A K, Obmrosi S, Rivera-Rios I. On pointwise and weighted estimates for commutators of CalderónZygmund operators. Adv Math, 2017, 319:153-181
[16] Lerner A K, Obmrosi S, Rivera-Rios I. Commutators of singular integral operators revisied. arXiv:1709.04724
[17] Li K. Sparse domination theorem for mltilinear singular integral operators with Lr-Hörmander condition. Michigan Math J, 2018, 67:253-265
[18] Li K, Moen K, Sun W. The sharp weighted bound for multilinear maximal functions and Calderón-Zygmund operators. J Four Anal Appl, 2014, 20:751-765
[19] Petermichl S. The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic. Amer J Math, 2007, 129:1355-1375
[20] Petermichl S. The sharp weighted bound for the Riesz transforms. Proc Amer Math Soc, 2008, 136:1237- 1249
[21] Rao M, Ren Z. Theory of Orlicz spaces//Monographs and Textbooks in Pure and Applied Mathematics, 146. New York:Marcel Dekker Inc, 1991
[22] Wilson M J. Weighted inequalities for the dyadic square function without dyadic A∞. Duke Math J, 1987, 55:19-50

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

	From	local

	Times	4
	Rate	100%

Abstract

109

Just accepted	Online first	Issue

0	0	109

	From	Others

	Times	109
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed