On embeddings of function classes defined by constructive characteristics

Tom 72 / 2006

Boris V. Simonov, Sergey Yu. Tikhonov Banach Center Publications 72 (2006), 285-307 MSC: Primary 46E35; Secondary 41A50, 26A33. DOI: 10.4064/bc72-0-19


In this paper we study embedding theorems for function classes which are subclasses of $L_p$, $1\le p\le \infty$. To define these classes, we use the notion of best trigonometric approximation as well as that of a $(\lambda,\beta)$-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.


  • Boris V. SimonovVolgograd State Technical University
    Volgograd, 400131, Russia
  • Sergey Yu. TikhonovCentre de Recerca Matematica (CRM)
    Bellaterra (Barcelona), E-08193, Spain

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