caa a22 4500 475740335 CHVBK 20180406123458.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/BF02674643 doi (NATIONALLICENCE)springer-10.1007/BF02674643 Bespalov M. Vladimir State University, USSR aut Permutations of the Walsh system that preserve Lebesgue constants [Elektronische Daten] [M. Bespalov] A class of permutations of the Walsh-Paley system that preserve the lebesgue constants and theL p -norms of the Dirichlet kernel is distinguished. Thus it is proved, in particular, that Fine's estimates and calculations of the Lebesgue constants for the Walsh—Paley system hold for the Walsh systems in the enumerations of Walsh and Kaczmarz. A third algorithm for calculating the Lebesgue constants, which is different from those obtained by Fine and which also makes it possible to calculate theL p -norms of the Dirichlet kernels, is proposed. It is shown that not all permutations of the Walsh system even within the blocks preserve the Lebesgue constants. The distinguished class of permutations includes theTW-systems of Schipp, which are not, in general, permutations within the blocks. Kluwer Academic/Plenum Publishers, 2000 Walsh—Paley system nationallicence Lebesgue constants nationallicence Dirichlet kernel nationallicence TW -systems nationallicence Mathematical Notes Springer Netherlands 68/1(2000-07-01), 32-42 0001-4346 68:1<32 2000 68 11006 https://doi.org/10.1007/BF02674643 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674643 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bespalov M. Vladimir State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Springer Netherlands 68/1(2000-07-01), 32-42 0001-4346 68:1<32 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer