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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, Volume 14, Issue 4(2), Pages 518–525 (Mi isu544)  

Mathematics

Embedding Theorems for $\mathbf{P}$-nary Hardy and $VMO$ Spaces

S. S. Volosivets

Saratov State University, 83, Astrakhanskaya str., Saratov, 410012, Russia

Abstract: In the present paper several embedding theorems of P. L. Ul'yanov type for Hölder spaces connected with $\mathbf{P}$-nary Hardy, $VMO$, $L^1$ and uniform metric on Vilenkin groups are proved. Its sharpness is also established. The sufficient conditions for the convergence of Fourier series with respect to multiplicative systems in Hardy space and uniform metric are also given.

Key words: $\mathbf{P}$-nary Hardy space, $\mathbf{P}$-nary $VMO$ space, embedding theorems, sharpness, uniform convergence.

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UDC: 517.518

Citation: S. S. Volosivets, “Embedding Theorems for $\mathbf{P}$-nary Hardy and $VMO$ Spaces”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 518–525

Citation in format AMSBIB
\Bibitem{Vol14}
\by S.~S.~Volosivets
\paper Embedding Theorems for $\mathbf{P}$-nary Hardy and $VMO$ Spaces
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2014
\vol 14
\issue 4(2)
\pages 518--525
\mathnet{http://mi.mathnet.ru/isu544}


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