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Abstract
Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems, some inequalities of martingale transform operator are obtained.
Abstract
Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w p Σα(X), w p Q α(X) and wD α(X). As applications of atomic decompositions, a sufficient condition for sublinear operators defined on some vector-valued weak martingale Hardy spaces to be bounded is given. In particular, some weak versions of martingale inequalities for the operators f*, S (p)(f) and σ(p)(f) are obtained.
We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H 1 to L 1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T 2 and R 2.
Abstract
Abstract
We consider Hausdorff operators generated by a function ϕ integrable in Lebesgue"s sense on either R or R 2, and acting on the real Hardy space H 1(R), or the product Hardy space H 11(R R), or one of the hybrid Hardy spaces H 10(R 2) and H 01(R 2), respectively. We give a necessary and sufficient condition in terms of ϕ that the Hausdorff operator generated by it commutes with the corresponding Hilbert transform.
In this paper the endpoint estimates for some multilinear operators related to certain sublinear integral operators on Herz and Herz type Hardy spaces are obtained. The operators include Littlewood-Paley operator and Marcinkiewicz operator.
Abstract
Обобщаются некоторы е дуальные результат ы теории мартингалов. Доказан ы теоремы дуальности а томических простран ств Харди, пространствBMO иVMO.
154 – 164 10.1016/j.jat.2008.11.014 . [11] Weisz , F. 2002 Summability of Multi-dimensional Fourier Series and Hardy Spaces Mathematics