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Garcia-Cuerva, J., Hardy spaces and Beurling algebras, J. London Math. Soc. 39 (1989), 499-513. Hardy spaces and Beurling algebras J. London Math. Soc

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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.

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Abstract  

Some atomic decomposition theorems are proved in vector-valued weak martingale Hardy spaces w pΣα(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.

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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.

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Abstract  

We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H 1, which may be considered over

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and
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. We also draw corollaries for the corresponding Hardy spaces over
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2 and
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2.

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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.

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Abstract  

We develop a Wold decomposition for the shift semigroup on the Hardy space

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}^2$$ \end{document}
of square summable Dirichlet series convergent in the half-plane
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. As an application we have that a shift invariant subspace of
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is unitarily equivalent to
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if and only if it has the form
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\phi \mathcal{H}^2$$ \end{document}
for some
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-inner function φ.

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Обобщаются некоторы е дуальные результат ы теории мартингалов. Доказан ы теоремы дуальности а томических простран ств Харди, пространствBMO иVMO.

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154 – 164 10.1016/j.jat.2008.11.014 . [11] Weisz , F. 2002 Summability of Multi-dimensional Fourier Series and Hardy Spaces Mathematics

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