Titlebook: Convergence and Summability of Fourier Transforms and Hardy Spaces; Ferenc Weisz Book 2017 Springer International Publishing AG 2017 Fejér

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One-Dimensional Hardy Spacesein [308, 309], Stein and Weiss [311], Lu [233], Uchiyama [340] and Grafakos [152]. Beyond these, the Hardy spaces have been introduced for martingales as well (see e.g. Garsia [127], Neveu [260], Dellacherie and Meyer [85, 86], Long [232] and Weisz [347]).

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2. Semiconvex Hulls of Compact Sets,similar results as in Chap. . For the restricted convergence, we use the Hardy space . and for the unrestricted .. We show that both maximal operators are bounded from the corresponding Hardy space to ., which implies the almost everywhere convergence. In both cases, the set of convergence is characterized as two types of Lebesgue points.

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https://doi.org/10.1007/979-8-8688-0500-4 analogous results to those of Sections .–. for higher dimensions. In the first section, we introduce the Fourier transform for functions and for tempered distributions and give the most important results. Since these proofs are very similar to those of the one-dimensional ones, we omit the proofs.

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https://doi.org/10.1007/979-8-8688-0500-4higher dimensional Fourier transforms. As in the literature, we investigate the three cases . = 1, . = 2 and . = .. The other type of summability, the so-called rectangular summability, will be investigated in the next chapter. Both types are general summability methods defined by a function .. We w

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https://doi.org/10.1007/978-3-319-56814-0Fejér summability; fourier analysis; hardy spaces; Lebesgue points; strong summability; harmonic analysis