Abstract:
A condition for a function of bounded type to belong to the Hardy class $H^1$ in terms of the Fourier transform of the boundary values of this function on $R^n$ is found. Applications of the obtained result to the theories of Hardy classes and of quasi-analytic classes of functions are given.
Citation:
F. A. Shamoyan, “Fourier transform and quasi-analytic classes of functions of bounded type on tubular domains”, Funktsional. Anal. i Prilozhen., 51:2 (2017), 97–100; Funct. Anal. Appl., 51:2 (2017), 157–160
\Bibitem{Sha17}
\by F.~A.~Shamoyan
\paper Fourier transform and quasi-analytic classes of functions of bounded type on tubular domains
\jour Funktsional. Anal. i Prilozhen.
\yr 2017
\vol 51
\issue 2
\pages 97--100
\mathnet{http://mi.mathnet.ru/faa3443}
\crossref{https://doi.org/10.4213/faa3443}
\elib{https://elibrary.ru/item.asp?id=29106596}
\transl
\jour Funct. Anal. Appl.
\yr 2017
\vol 51
\issue 2
\pages 157--160
\crossref{https://doi.org/10.1007/s10688-017-0179-y}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85020788450}
Linking options:
https://www.mathnet.ru/eng/faa3443
https://doi.org/10.4213/faa3443
https://www.mathnet.ru/eng/faa/v51/i2/p97
This publication is cited in the following 1 articles:
F. A. Shamoyan, “Boundary quasianalyticity and a Phragmén–Lindelöf type theorem in classes of functions of bounded type in tubular domains”, St. Petersburg Math. J., 33:6 (2022), 1035–1046