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

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2296-5009 cent results from the past 20-30 years.Considers strong summThis book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, whic

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System Requirements and Licensing,. are very similar to those for the one-dimensional . spaces studied in Chap. ., so we omit the corresponding proofs. However, the proofs for . are different from the one-dimensional version requiring new ideas. We also study some generalizations of the Hardy-Littlewood maximal function for multi-dimensional functions.

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https://doi.org/10.1007/979-8-8688-0500-4gular Dirichlet integrals. Using the analogous results for the partial sums of multi-dimensional Fourier series proved in Section 4.2, we show that the Dirichlet integrals converge in the .-norm to the function (1 < . < .). The multi-dimensional version of Carleson’s theorem is also verified.

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One-Dimensional Fourier Transforms . < .). The proof of Carleson’s theorem, i.e. that of the almost everywhere convergence can be found in Carleson [52], Grafakos [152], Arias de Reyna [8], Muscalu and Schlag [253], Lacey [207] or Demeter [88].

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Book 2017y spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the Fejér, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations. .Following on the classic books by Bary (1964) and Zygmund (1968), th

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