Strong approximation by Fourier series and generalized periodic Nikol’skij-Besov-Morrey spaces

Zhuldyz Baituyakova, Dauren Matin, Meruert Ilyasova

2018

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DOI 10.1063/1.5049081
Data confidence 70 medium
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Abstract

In recent years, a lot of attention has been paid to study of Morrey type spaces. Many applications in partial differential equation of Morrey spaces and Nikol’skij-Besov spaces have been given in the work of G. Di Fazioand, M. Ragua and the book of T. Mizuhara. The theory of generalized Nikol’skij-Besov-Morrey spaces is developed. Generalized Morrey spaces, proposed by T. Mizuhara and E. Nakai, are equipped with a parameter and a function In the present paper we study Nikol’skij-Besov spaces on scale generalized periodic Morrey space. Finally, we get an interesting char-acterization of the space Nφ,p,qs(T) by using differences of partial sums of the Fourier series and consequence for strong approximation of Fourier series on Morrey space.