$L^{p}-$estimates for uncentered spherical averages and lacunary maximal functions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929474999681024 |
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| author | Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh Shuin, Kalachand |
| author_facet | Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh Shuin, Kalachand |
| contents | The primary goal of this paper is to introduce bilinear analogues of uncentered spherical averages, Nikodym averages associated with spheres and the associated bilinear maximal functions. We obtain $L^p$-estimates for uncentered bilinear maximal functions for dimensions $d\geq2$. Moreover, we also discuss the one-dimensional case. In the process of developing these results, we also establish new and interesting results in the linear case. In particular, we will prove $L^p$-improving properties for single scale averaging operators and $L^p$-estimates for lacunary maximal functions in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06978 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L^{p}-$estimates for uncentered spherical averages and lacunary maximal functions Bhojak, Ankit Choudhary, Surjeet Singh Shrivastava, Saurabh Shuin, Kalachand Classical Analysis and ODEs 42B25, 42B15 The primary goal of this paper is to introduce bilinear analogues of uncentered spherical averages, Nikodym averages associated with spheres and the associated bilinear maximal functions. We obtain $L^p$-estimates for uncentered bilinear maximal functions for dimensions $d\geq2$. Moreover, we also discuss the one-dimensional case. In the process of developing these results, we also establish new and interesting results in the linear case. In particular, we will prove $L^p$-improving properties for single scale averaging operators and $L^p$-estimates for lacunary maximal functions in this context. |
| title | $L^{p}-$estimates for uncentered spherical averages and lacunary maximal functions |
| topic | Classical Analysis and ODEs 42B25, 42B15 |
| url | https://arxiv.org/abs/2310.06978 |