Author:
Saker S. H.,Mahmoud R. R.,Hassan M. H.
Abstract
UDC 517.5
We prove some relations between the discrete Gehring classes
𝒢
q
and the discrete Muckenhoupt classes
𝒜
p
.
Specifically, by using some known Hardy-type and Carleman-type inequalities, we study the relationship between
𝒢
1
,
𝒜
∞
and
𝒜
1
for nonincreasing and nondecreasing weights. Finally, we establish some general results by introducing the notions of
𝒢
φ
classes defined for nonnegative convex function
φ
.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference16 articles.
1. G. Bennett, K.-G. Grosse-Erdmann, Weighted Hardy inequalities for decreasing sequences and functions, Math. Ann., 334, 489–531 (2006).
2. A. Böttcher, M. Seybold, Wackelsatz and Stechkin's inequality for discrete Muckenhoupt weights, Preprint № 99-7, TU Chemnitz (1999).
3. G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, 2nd ed., Cambridge Univ. Press (1934).
4. N. Levinson, Generalizations of an inequality of Hardy, Duke Math. J., 31, № 3, 389–394 (1964).
5. M. M. Iddrisu, C. A. Okpoti, Applications of Taylor series for Carleman's inequality through Hardy inequality, Korean J. Math., 23, № 4, 655–664 (2015).