naa a22 4500 510811310 CHVBK 20180411083443.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1134/S0081543813080063 doi (NATIONALLICENCE)springer-10.1134/S0081543813080063 Estimation of the uniform modulus of continuity of the generalized Bessel potential [Elektronische Daten] [M. Goldman, A. Malysheva] We study generalized Bessel potentials constructed by means of convolutions of functions with kernels that generalize the classical Bessel-Macdonald kernels. In contrast to the classical case, nonpower singularities of kernels in a neighborhood of the origin are admitted. The integral properties of functions are characterized in terms of decreasing rearrangements. The differential properties of potentials are described by the kth-order moduli of continuity in the uniform norm. An order-sharp upper estimate is established for the modulus of continuity of a potential. Such estimates play an important role in the theory of function spaces. They allow one to establish sharp embedding theorems for potentials, find majorants of the moduli of continuity, and estimate the approximation numbers of embedding operators. Pleiades Publishing, Ltd., 2013 Goldman M. Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia aut Malysheva A. Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia aut Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 75-86 0081-5438 283:1<75 2013 283 11501 https://doi.org/10.1134/S0081543813080063 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813080063 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Goldman M. Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia aut NATIONALLICENCE 700 1- Malysheva A. Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, 117198, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 283/1(2013-12-01), 75-86 0081-5438 283:1<75 2013 283 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer