Weighted Inequalities for a Superposition of the Copson Operator and the Hardy Operator
[ X ]
Tarih
2022
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Birkhauser
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We study a three-weight inequality for the superposition of the Hardy operator and the Copson operator, namely (integral(b)(a)(integral(b)(t)integral(s)(a) f(tau)p upsilon(tau)d tau)(q/p) u(s) ds)(r/q)w(t)dt)(1/r) <= C integral(b)(a) f(t) dt, in which (a, b) is any nontrivial interval, q, r are positive real parameters and p is an element of (0, 1]. A simple change of variables can be used to obtain any weighted L-p-norm with p >= 1 on the right-hand side. Another simple change of variables can be used to equivalently turn this inequality into the one in which the Hardy and Copson operators swap their positions. We focus on characterizing those triples of weight functions (u, v, w) for which this inequality holds for all nonnegative measurable functions f with a constant independent of f. We use a newtype of approach based on an innovative method of discretization which enables us to avoid duality techniques and therefore to remove various restrictions that appear in earlier work. This paper is dedicated to Professor Stefan Samko on the occasion of his 80th birthday.
Açıklama
Anahtar Kelimeler
Weighted Hardy inequality; Superposition of operators; Copson operator; Hardy operator; 26D10
Kaynak
Journal of Fourier Analysis and Applications
WoS Q Değeri
Q3
Scopus Q Değeri
Q2
Cilt
28
Sayı
2
