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• Author or Editor: H. Kita
Clear All Modify Search  # On Interpolation of the Fourier Maximal Operator in Orlicz Spaces

Acta Mathematica Hungarica
Author: H. Kita
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# On Maximal Operator of Partial Sums of Fourier Series in Orlicz Spaces

Acta Mathematica Hungarica
Author: H. Kita
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# On an interpolation theorem of Hunt-Sjölin

Acta Mathematica Hungarica
Author: H. Kita
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# A reverse weighted inequality for the Hardy-Littlewood maximal function in Orlicz spaces

Acta Mathematica Hungarica
Author: H. Kita

## Abstract

Let Φ(t)= ∫_0^t a(s) ds and Ψ(t)= ∫_0^t b(s) ds, where a(s) is a positive continuous function such that ∫_0^1 \frac{a(s)}{s} ds < ∞and ∫_1^{\∞}\frac{a(s)}{s} ds= +\∞, and b(s) is an increasing function such that \lim_{s\to\∞}b(s)= +\∞. Letw be a weight function and suppose that w∈A1\∩ A'. Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent:(I) there exist positive constants C 1 and C 2 such that

\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} $$\int_0^s {\frac{{a\left( t \right)}}{t}dt \geqq } C_1 b\left( {C_2 s} \right)foralls > 0;$$ \end{document}
(II) there exist positive constants C 3 and C 4 such that
\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} $$\int {_{R^n } } \Psi \left( {C_3 \left| {f\left( x \right)} \right|} \right)w\left( x \right)dx \leqq C_4 \int {_{R^n } } \Phi \left( {Mf\left( x \right)} \right)w\left( x \right)dxforallf \in {\mathcal{R}}_0 \left( w \right)$$ \end{document}

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# Convergence of fourier series of a function on generalized Wiener's classBV (p(n↑∞)

Acta Mathematica Hungarica
Author: H. Kita
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# Almost everywhere convergence of orthogonal series

Acta Mathematica Hungarica
Author: H. Kita
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# Inequalities with weights for maximal functions in orlicz spaces

Acta Mathematica Hungarica
Author: H. Kita
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# On quasi ϕ(L)*-a.e. convergence of Fourier series of functions in Orlicz spaces

Acta Mathematica Hungarica
Authors: H. Kita and K. Yoneda
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# A generalization of bounded variation

Acta Mathematica Hungarica
Authors: H. Kita and K. Yoneda
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