Embedding Schramm spaces into Chanturiya classes

Abstract

The main theorem of this paper establishes a necessary and sufficient condition for embedding Schramm spaces $$\varPhi BV$$ into Chanturiya classes $$V[\nu ]$$ . This result is new even for the classical spaces in the theory of Fourier series, namely, for the Wiener and the Salem classes. Furthermore, it provides a characterization of the embedding of Waterman classes $$\varLambda BV$$ into $$V[\nu ]$$ . As a by-product of the main result, we establish a convergence criterion for the Fourier series of functions of $$\varPhi BV$$ ; this is an extension of a well-known result due to Salem. An estimate on the magnitude of the Fourier coefficients in the space $$\varPhi BV$$ is also given, and finally it is shown that some of these results can be extended to a more general setting.