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Showing 1 to 3 of 3 for “"Maximal operator"”.
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Weighted Norm Inequalities for the Maximal Operator on Variable Lebesgue Spaces Over Spaces of Homogeneous Type
… norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces $L^\pp$. We prove that the variable Muckenhoupt condition $\App$ is necessary and sufficient for the strong type inequality if $\pp$ satisfies log-H\"older continuity conditions and $1 < …
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Almost everywhere convergence of dyadic partial sums of Fourier series for almost periodic functions
… is presented by way of a bound on an appropriate maximal operator for \(p\) = 2\(^k\), \(k\) \(\in\) \(\char{bbold10}{0x4E}\). In the process of establishing this, a number of general results are obtained that will facilitate further work pertaining to operator bounds and convergence issues in …
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Sparse technology in weighted harmonic analysis
… the Muckenhoupt-Wheeden conjectures for sparse operators. More specifically, we will construct a pair of weights $(u,v)$ for which the Hardy-Littlewood maximal function is bounded from $L^p(v)$ to $L^p(u)$ and from $L^{p'}(u^{1-p'})$ to $L^{p'}(v^{1-p'})$ while a dyadic sparse operator is not …