On grand Sobolev spaces and pointwise description of Banach function spaces

On grand Sobolev spaces and pointwise description of Banach function spaces Full article

Journal

Nonlinear Analysis, Theory, Methods and Applications
ISSN: 0362-546X

Output data

Year: 2021, Volume: 202, Article number : 112100, Pages count : 17 DOI: 10.1016/j.na.2020.112100

Tags

primary 46E30, secondary 46E35 Banach function space, Grand Sobolev space, Maximal function, Pointwise description

Authors

Jain Pankaj ¹ , Molchanova Anastasia ^2,3 , Singh Monika ⁴ , Vodopyanov Sergey ²

Affiliations

1	Department of Mathematics, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi 110 021, India
2	Sobolev Institute of Mathematics, Academic Koptyug avenue 4, 630090 Novosibirsk, Russia
3	Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8–10, 1040 Wien, Austria
4	Department of Mathematics, Lady Shri Ram College For Women (University of Delhi), Lajpat Nagar, New Delhi 110 024, India

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy–Littlewood maximal operator is bounded. We also study weighted grand Sobolev spaces, defined on arbitrary open sets Ω (of finite or infinite measure) in Rn, and provide pointwise description of them.

Jain P. , Molchanova A. , Singh M. , Vodopyanov S.
On grand Sobolev spaces and pointwise description of Banach function spaces
Nonlinear Analysis, Theory, Methods and Applications. 2021. V.202. 112100 :1-17. DOI: 10.1016/j.na.2020.112100 WOS Scopus OpenAlex

Submitted:	Jun 4, 2020
Accepted:	Aug 12, 2020

Web of science:	WOS:000581179100005
Scopus:	2-s2.0-85089805830
OpenAlex:	W3082384222

DB	Citing
Scopus	10
OpenAlex	9
Web of science	8