Estimates for continuity envelopes and approximation numbers of Bessel potentials

In this paper we study spaces of Bessel potentials in n-dimensional Euclidean spaces. They are constructed on the basis of a rearrangement-invariant space (RIS) by using convolutions with Bessel-MacDonald kernels. Specifically, the treatment covers spaces of classical Bessel potentials. We establish two-sided estimates for the corresponding modulus of smoothness of order k∈N, ωk (f ; t), and determine their continuity envelope functions. This result is then applied to estimate the approximation numbers of some embeddings. © 2013 Elsevier Inc.

Авторы
Редакторы
-
Издательство
-
Номер выпуска
-
Язык
Английский
Страницы
58-85
Статус
Опубликовано
Подразделение
-
Номер
-
Том
172
Год
2013
Организации
  • 1 Peoples Friendship University of Russia, Department of Mathematical Analysis and Function Theory, Miklukho Maklai 6, Moscow 117198, Russian Federation
  • 2 Mathematical Institute, Friedrich-Schiller-University Jena, D-07737 Jena, Germany
Ключевые слова
Approximation numbers; Compact embeddings; Continuity envelopes; Convolution; Rearrangement invariant space; Space of potentials
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/2032/