Weighted norm inequalities for integral transforms with splitting kernels
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911978450059264 |
|---|---|
| author | Pinos, Alberto Debernardi |
| author_facet | Pinos, Alberto Debernardi |
| contents | We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable.
The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the $\mathscr{H}_α$ (or Struve) transform in the case $α>\frac{1}{2}$, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases $p=1$ or $q=\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16536 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weighted norm inequalities for integral transforms with splitting kernels Pinos, Alberto Debernardi Classical Analysis and ODEs Functional Analysis Primary: 42A38. Secondary: 26D15, 44A15 We obtain necessary and sufficient conditions on weights for a wide class of integral transforms to be bounded between weighted $L^p-L^q$ spaces, with $1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are only assumed to satisfy upper bounds given by products of two functions, one in each variable. The obtained results are applicable to a number of transforms, some of which are included here as particular examples. Some of the new results derived here are the characterization of weights for the boundedness of the $\mathscr{H}_α$ (or Struve) transform in the case $α>\frac{1}{2}$, or the characterization of power weights for which the Laplace transform is bounded in the limiting cases $p=1$ or $q=\infty$. |
| title | Weighted norm inequalities for integral transforms with splitting kernels |
| topic | Classical Analysis and ODEs Functional Analysis Primary: 42A38. Secondary: 26D15, 44A15 |
| url | https://arxiv.org/abs/2312.16536 |