Criteria for the boundedness of a certain class of matrix operators from lpv into lqu

Ainur Temirkhanova, Aigul Beszhanova

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2023

Full text Open access: Gold Metadata (CSL-JSON)

DOI 10.31489/2023m3/122-137

Data confidence 70 medium

How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

One of the main aims in the theory of matrices is to find necessary and sufficient conditions for the elements of any matrix so that the corresponding matrix operator maps continuously from one normed space into another one. Thus, it is very important to find the norm of the matrix operator, at least, to find upper and lower estimates of it. This problem in Lebesgue spaces of sequences in the general case is still open. This paper deals with the problem of boundedness of matrix operators from lpv into lqu for 1 < q < p < ∞, and we obtain necessary and sufficient conditions of this problem when matrix operators belong to the classes O2+- satisfying weaker conditions than Oinarov’s condition.