Kolyada inequality for partial moduli of smoothness of functions with lacunary Fourier coefficients

Autor: Simonov, Boris V., Simonova, Irina E., Ivanyuk, Vera A.

Publikováno v: Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, Vol 22, Iss 4, Pp 447-457 (2022)

The problem of estimating the moduli of smoothness of functions from $L_q$ in terms of moduli of smoothness from $L_p$ is well known. The initial stage in estimating the moduli of smoothness was the study of properties of functions from Lipschitz c

Externí odkaz: https://doaj.org/article/8c3a5429c9da4cca95488b9600422d5c

Embedding theorems of funcitional classes, III

Autor: Simonov, Boris V., Tikhonov, Sergey Yu., Centre de Recerca Matemàtica

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::fcdca36ded44191a045b4f5060d9d557
http://hdl.handle.net/2072/418790

Norm inequalities in multidimensional Lorentz spaces

Autor: Simonov, Boris V., Tikhonov, Sergey Yu., Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::5c771b82acf136deaa49838f54ece64c
https://ddd.uab.cat/record/44052