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- W1998057770 abstract "A new atomic decomposition of the two-parameter dyadic martingale Hardy spacesHpdefined by the quadratic variation is given. We introduceHp-quasi-local operators and prove that if a sublinear operatorVisHp-quasi-local and bounded fromL2toL2then it is also bounded fromHptoLp(0<p⩽1). By an interpolation theorem we get thatVis of weak type (H#1, L1) where the Hardy spaceH#1is defined by the hybrid maximal function. As an application it is shown that the maximal operator of the Cesàro means of a two-parameter martingale is bounded fromHptoLp(4/5<p⩽∞) and is of weak type (H#1, L1). So we obtain that the Cesàro means of a functionf∈H#1converge a.e. to the function in question. Finally, it is verified that if the supremum is taken over all two-powers, only, then the maximal operator of the Cesàro means is bounded fromHptoLpfor every 2/3<p⩽∞." @default.
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- W1998057770 date "1997-02-01" @default.
- W1998057770 modified "2023-10-11" @default.
- W1998057770 title "Cesàro Summability of Two-Parameter Walsh–Fourier Series" @default.
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- W1998057770 doi "https://doi.org/10.1006/jath.1996.3021" @default.
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