naa a22 4500 510811647 CHVBK 20180411083445.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813010112 doi (NATIONALLICENCE)springer-10.1134/S0081543813010112 Global and local smoothness of the Hilbert transforms [Elektronische Daten] [Mikhail Dyachenko, Erlan Nursultanov, Sergey Tikhonov] We study the smoothness properties of the Hilbert transform in terms of the smoothness of the function itself. We prove global and local analogues of Privalov's theorem. The sharpness of these results is shown. Pleiades Publishing, Ltd., 2013 Dyachenko Mikhail Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut Nursultanov Erlan L.N. Gumilyov Eurasian National University, Munaitpasov str. 2, 010008, Astana, Kazakhstan aut Tikhonov Sergey Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010, Barcelona, Spain aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 169-180 0081-5438 280:1<169 2013 280 11501 https://doi.org/10.1134/S0081543813010112 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813010112 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dyachenko Mikhail Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 700 1- Nursultanov Erlan L.N. Gumilyov Eurasian National University, Munaitpasov str. 2, 010008, Astana, Kazakhstan aut NATIONALLICENCE 700 1- Tikhonov Sergey Institució Catalana de Recerca i Estudis Avançats, Passeig Lluis Companys 23, 08010, Barcelona, Spain aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 169-180 0081-5438 280:1<169 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer