논문KCI 등재
Two Weight Estimate for the Paraproduct in the Space of Homogeneous Type
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In this paper, we provide sufficient conditions of a pair of weights (u, v) and a function b so that the dyadic paraproduct is bounded from L2u(X) into L2v(X), where X is a space of homegeneous type. In order to prove the main result we use the honest dyadic system introduced in [10].
Abstract
In this paper, we provide sufficient conditions of a pair of weights (u, v) and a function b so that the dyadic paraproduct is bounded from L2u(X) into L2v(X), where X is a space of homegeneous type. In order to prove the main result we use the honest dyadic system introduced in [10].
참고문헌 (11)
- R. Coifman, "Analyse harmonique non-commutative sur certains espaces homogenes" (1971), Springer-Verlag Berlin Heidelberg
- O. Beznosova, "Linear bound for the dyadic paraproduct on weighted Lebesgue space L2(w)", J. Func. Anal, 255, pp.994~1007 (2008)
- O. Beznosova, "Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 2)", pp.135~169 (2017), Springer International Publishing
- M. Christ, "A T(b) theorem with remarks on analytic capacity and the Cauchy integral", Colloq. Math, 60, pp.61 (1990), 601~628
- D. Chung, "Weighted inequalities for multivariable dyadic paraproducts", Publ. Mat, 55, pp.475~499 (2011)
- 정대원, "ON A TWO WEIGHTS ESTIMATE FOR THE COMMUTATOR", East Asian Mathematical Journal, 33(1), pp.103~113 (2017), 영남수학회[DOI]
- M.C. Pereyra, "Dyadic harmonic analysis and weighted inequalities: the sparse revolution arXiv preprint arXiv:1812.00850v1", ~ (2018)
- T. Hytonen, "Systems of dyadic cubes in a doubling metric space", Colloq. Math, 126, pp.1~33 (2012)
- F. Nazarov, "The Bellman functions and the two-weight inequal-ities for Haar Multipliers", Journal of the AMS, 12, pp.909~928 (1992)
- D.Weirich, "Weighted Inequalities for Dyadic Operators over Space of Homogeneous Type", Ph.D, pp.2017
- M. Wilson, "Weighted inequalities for the dyadic square function without dyadic A1", Duke Math. J, 55, pp.19~49 (1987)
관련 논문AI추천
NOTES ON SAWYER TYPE ESTIMATES FOR THE DYADIC PARAPRODUCT정대원영남수학회 · East Asian Mathematical Journal2023 · 제39권 제3호A Note on Two Weight Inequalities for the Dyadic Paraproduct정대원영남수학회 · East Asian Mathematical Journal2020 · 제36권 제3호Weighted norm estimates for the dyadic paraproduct with VMO function정대원대한수학회 · 대한수학회보2021 · 제58권 제1호ON QUANTITATIVE TWO WEIGHT ESTIMATES FOR SOME DYADIC OPERATORS정대원영남수학회 · East Asian Mathematical Journal2022 · 제38권 제3호Some Multi-sublinear Operators on generalized Morrey spaces with non-doubling measuresXiangxing Tao, Yanlong Shi대한수학회 · 대한수학회지2012 · 제49권 제5호Weighted vector-valued bounds for a class of multilinear singular integral operators and applicationsGuo-En Hu, Jiecheng Chen대한수학회 · 대한수학회지2018 · 제55권 제3호
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