Weighted Weak Type estimates for non-integral Square Functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911010655305728 |
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| author | Mena, Dario Reguera, Maria Carmen Roncal, Luz |
| author_facet | Mena, Dario Reguera, Maria Carmen Roncal, Luz |
| contents | We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse Hölder constants associated to the weight. The method of proof uses a decoupling of the role of the weights via a quantitative version of Gehring's lemma. The results can be extended to other $p$ in the range of boundedness of the square function at hand. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Weak Type estimates for non-integral Square Functions Mena, Dario Reguera, Maria Carmen Roncal, Luz Classical Analysis and ODEs 42B25 (Primary), 42B20, 42B35 (Secondary) We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the $A_p$ and reverse Hölder constants associated to the weight. The method of proof uses a decoupling of the role of the weights via a quantitative version of Gehring's lemma. The results can be extended to other $p$ in the range of boundedness of the square function at hand. |
| title | Weighted Weak Type estimates for non-integral Square Functions |
| topic | Classical Analysis and ODEs 42B25 (Primary), 42B20, 42B35 (Secondary) |
| url | https://arxiv.org/abs/2506.14897 |