Geodesic
Embedding Theorems for $\mathbf{P}$-nary Hardy and $VMO$ Spaces
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 518-525

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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. 
@article{ISU_2014_14_4_a4,
     author = {S. S. Volosivets},
     title = {Embedding {Theorems} for $\mathbf{P}$-nary {Hardy} and $VMO$ {Spaces}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {518--525},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a4/}
}
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S. S. Volosivets. Embedding Theorems for $\mathbf{P}$-nary Hardy and $VMO$ Spaces. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 518-525. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a4/