Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality
In this paper, we will prove some fundamental properties of the discrete power mean operator Mpun=1/n∑k=1n upk1/p,for n∈I⊆ℤ+, of order p, where u is a nonnegative discrete weight defined on I⊆ℤ+ the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5515042 |
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| author | S. H. Saker S. S. Rabie R. P. Agarwal |
| author_facet | S. H. Saker S. S. Rabie R. P. Agarwal |
| author_sort | S. H. Saker |
| collection | DOAJ |
| description | In this paper, we will prove some fundamental properties of the discrete power mean operator Mpun=1/n∑k=1n upk1/p,for n∈I⊆ℤ+, of order p, where u is a nonnegative discrete weight defined on I⊆ℤ+ the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of different operators with different powers. Next, we will study the structure of the generalized discrete class BpqB of weights that satisfy the reverse Hölder inequality Mqu≤BMpu, for positive real numbers p, q, and B such that 0<p<q and B>1. For applications, we will prove some self-improving properties of weights from BpqB and derive the self improving properties of the discrete Gehring weights as a special case. The paper ends by a conjecture with an illustrative sharp example. |
| format | Article |
| id | doaj-art-17c32d33706a424a87b2ba5cbb4dbcc3 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-17c32d33706a424a87b2ba5cbb4dbcc32025-08-20T03:54:20ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/55150425515042Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s InequalityS. H. Saker0S. S. Rabie1R. P. Agarwal2Mathematics Division, Faculty of Advanced Basic Sciences, Galala University, Galala New City, EgyptDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Texas A & M University-Kingsville, TX 78363, USAIn this paper, we will prove some fundamental properties of the discrete power mean operator Mpun=1/n∑k=1n upk1/p,for n∈I⊆ℤ+, of order p, where u is a nonnegative discrete weight defined on I⊆ℤ+ the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of different operators with different powers. Next, we will study the structure of the generalized discrete class BpqB of weights that satisfy the reverse Hölder inequality Mqu≤BMpu, for positive real numbers p, q, and B such that 0<p<q and B>1. For applications, we will prove some self-improving properties of weights from BpqB and derive the self improving properties of the discrete Gehring weights as a special case. The paper ends by a conjecture with an illustrative sharp example.http://dx.doi.org/10.1155/2021/5515042 |
| spellingShingle | S. H. Saker S. S. Rabie R. P. Agarwal Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality Journal of Function Spaces |
| title | Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality |
| title_full | Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality |
| title_fullStr | Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality |
| title_full_unstemmed | Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality |
| title_short | Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality |
| title_sort | properties of a generalized class of weights satisfying reverse holder s inequality |
| url | http://dx.doi.org/10.1155/2021/5515042 |
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