On local properties of singular integral

J. I.  Mamedkhanov; S. Z.  Jafarov

doi:10.37863/umzh.v75i5.6959

J. I. Mamedkhanov Baku State University, Azerbaijan
S. Z. Jafarov Muş Alparslan University, Turkey and Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku

DOI: https://doi.org/10.37863/umzh.v75i5.6959

Keywords: Regular curve, singular integral, H\H, local class of functios, Plemelj-Privalov theorem

Abstract

UDC 517.5

Let $\gamma$ be a regular curve. We study the local properties of singular integrals in the $H_{\alpha }^{\alpha +\beta }(t_{0},\gamma)$ class of functions. We obtain a strengthening of the Plemelj\–Privalov theorem for functions from the class $H_{\alpha }^{\alpha +\beta}(t_{0},\gamma).$ It is proved that, at the point $t_{0},$ of increased smoothness for $\alpha +\beta < 1,$ there is only a logarithmic loss.

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