ON QUANTITATIVE TWO WEIGHT ESTIMATES FOR SOME DYADIC OPERATORS
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In this paper, a comparison of two types of quantitative two weight conditions for the boundedness of the dyadic paraproduct and the commutator of the Hilbert transform is provided. In the case of the com- mutator [b, H], the conditions of the well-known Bloom’s inequality [2] and the slightly different types of two weight inequality introduced in [1] are compared around the A2-conditions on weights and the novel conditions on the function b .
Abstract
In this paper, a comparison of two types of quantitative two weight conditions for the boundedness of the dyadic paraproduct and the commutator of the Hilbert transform is provided. In the case of the com- mutator [b, H], the conditions of the well-known Bloom’s inequality [2] and the slightly different types of two weight inequality introduced in [1] are compared around the A2-conditions on weights and the novel conditions on the function b .
참고문헌 (10)
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- S. Bloom, "A commutator theorem and weighted BMO", Trans. Amer. Math. Soc, 292(1), pp.103~122 (1985)
- D. Chung, "Sharp estimates for the commutators of the Hilbert, Riesz transforms and the Beurling-Ahlfors operator on weighted Lebsgue spaces", Indiana Univ. Math. Journal, 60(5), pp.1543~1588 (2011)
- 정대원, "ON A TWO WEIGHTS ESTIMATE FOR THE COMMUTATOR", East Asian Mathematical Journal, 33(1), pp.103~113 (2017), 영남수학회[DOI]
- I. Holmes, "Blooms inequality: commutators in a two-weight setting", Arch. Math, 106(1), pp.53~63 (2016)
- I. Holmes, "Commutators in the two-weight setting", Math. Ann (2016)[DOI]
- T. Hytönen, "Systems of dyadic cubes in a doubling metric space", Colloq. Math, 126, pp.1~33 (2012)
- J. C. Moraes, "Weighted estimates for dyadic operators with complexity", PhD, pp.2011
- J. C. Moraes, "Weighted estimates for dyadic Paraproduct and t-Haar multiplies with complexity (m, n)", Publ. Mat, 57, pp.265~294 (2013)
- F. Nazarov, "The Bellman functions and the two-weight inequal-ities for Haar Multipliers", Journal of the AMS, 12, pp.909~928 (1992)