Some New Sobolev-Type Theorems for the Rough Riesz Potential Operator on Grand Variable Herz Spaces
In this paper, our first objective is to define the idea of grand variable Herz spaces. Then, our main goal is to prove boundedness results for operators, including the rough Riesz potential operator of variable order and the fractional Hardy operators, on grand variable Herz spaces under some prope...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/11/1873 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, our first objective is to define the idea of grand variable Herz spaces. Then, our main goal is to prove boundedness results for operators, including the rough Riesz potential operator of variable order and the fractional Hardy operators, on grand variable Herz spaces under some proper assumptions. To prove the boundedness results, we use Holder-type and Minkowski inequalities. In the proof of the main result, we use different techniques. We divide the summation into different terms and estimate each term under different conditions. Then, by combining the estimates, we prove that the rough Riesz potential operator of variable order and the fractional Hardy operators are bounded on grand variable Herz spaces. It is easy to show that the rough Riesz potential operator of variable order generalizes the Riesz potential operator and that the fractional Hardy operators are generalized versions of simple Hardy operators. So, our results extend some previous results to the more generalized setting of grand variable Herz spaces. |
|---|---|
| ISSN: | 2227-7390 |