Hardy Spaces on the Plane and Double Fourier Transforms |
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Authors: | Dang Vu Giang Ferenc Moricz |
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Institution: | (1) Institute of Mathematics, University of Veszprem, Egyetem U. 10, 8201 Veszprem, Hungary;(2) Bolyai Institute, University of Szeged, Aradi Vertanuk Tere 1, 6720 Szeged, Hungary |
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Abstract: | We provide a direct computational proof of the known inclusion
where
is the product Hardy space defined for example by R. Fefferman and
is the classical Hardy space used, for example, by E.M. Stein. We
introduce a third space
of Hardy type and analyze the interrelations among these spaces. We give simple sufficient conditions for a given function
of two variables to be the double Fourier transform of a function in
and
respectively. In particular, we obtain a broad class of multipliers on
and
respectively. We also present analogous sufficient conditions in the case of double trigonometric series and, as a by-product,
obtain new multipliers on
and
respectively. |
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Keywords: | |
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