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Weierstrass and Picard summability of more-dimensional Fourier transforms
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Ferenc Weisz
Published/Copyright:
November 22, 2012
Abstract
It is proved that the maximal operator of the Weierstrass and Picard summability means of a tempered distribution is bounded from Hp(ℝd) to Lp(ℝd) for all 0 < p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the summability means of a function f ∈ L1(ℝd) converge a.e. to f. Similar results are shown for conjugate functions and for Fourier series.
Published Online: 2012-11-22
Published in Print: 2012-11
© by Oldenbourg Wissenschaftsverlag, München, Germany
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- Schur-harmonic convexity for differences of some means
- Weierstrass and Picard summability of more-dimensional Fourier transforms
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- On the strong unique continuation property of uniformly elliptic differential equations in the plane
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Articles in the same Issue
- Schur-harmonic convexity for differences of some means
- Weierstrass and Picard summability of more-dimensional Fourier transforms
- Explicit construction of M-band tight framelet packets
- On the strong unique continuation property of uniformly elliptic differential equations in the plane
- Integral and series representations of the digamma and polygamma functions
