Convergence of Fourier series at or beyond endpoint

Mathematics – Classical Analysis and ODEs

Scientific paper

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20 pages

Scientific paper

We consider several problems at or beyond endpoint in harmonic analysis. The solutions of these problems are related to the estimates of some classes of sublinear operators. To do this, we introduce some new functions spaces $RL^{p,s}_{|x|^{\alpha}}({\bf R}^n)$ and $\dot{R}L^{p,s}_{|x|^{\alpha}}({\bf R}^n)$, which play an analogue role with the classical Hardy spaces $H^p({\bf R}^n)$. These spaces are subspaces of $L^p_{|x|^{\alpha}}({\bf R}^n)$ with $1

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