Asymptotically sharp reverse Hölder inequalities for flat Muckenhoupt weights
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2016
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| _version_ | 1866913508537401344 |
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| author | Parissis, Ioannis Rela, Ezequiel |
| author_facet | Parissis, Ioannis Rela, Ezequiel |
| contents | We present reverse Hölder inequalities for Muckenhoupt weights in $\mathbb{R}^n$ with an asymptotically sharp behavior for flat weights, namely $A_\infty$ weights with Fujii-Wilson constant $(w)_{A_\infty}\to 1^+$. That is, the local integrability exponent in the reverse Hölder inequality blows up as the weight becomes nearly constant. This is expressed in a precise and explicit computation of the constants involved in the reverse Hölder inequality. The proofs avoid BMO methods and rely instead on precise covering arguments. Furthermore, in the one-dimensional case we prove sharp reverse Hölder inequalities for one-sided and two sided weights in the sense that both the integrability exponent as well as the multiplicative constant appearing in the estimate are best possible. We also prove sharp endpoint weak-type reverse Hölder inequalities and consider further extensions to general non-doubling measures and multiparameter weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_01932 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Asymptotically sharp reverse Hölder inequalities for flat Muckenhoupt weights Parissis, Ioannis Rela, Ezequiel Classical Analysis and ODEs 42B25 (Primary), 42B35 (Secondary) We present reverse Hölder inequalities for Muckenhoupt weights in $\mathbb{R}^n$ with an asymptotically sharp behavior for flat weights, namely $A_\infty$ weights with Fujii-Wilson constant $(w)_{A_\infty}\to 1^+$. That is, the local integrability exponent in the reverse Hölder inequality blows up as the weight becomes nearly constant. This is expressed in a precise and explicit computation of the constants involved in the reverse Hölder inequality. The proofs avoid BMO methods and rely instead on precise covering arguments. Furthermore, in the one-dimensional case we prove sharp reverse Hölder inequalities for one-sided and two sided weights in the sense that both the integrability exponent as well as the multiplicative constant appearing in the estimate are best possible. We also prove sharp endpoint weak-type reverse Hölder inequalities and consider further extensions to general non-doubling measures and multiparameter weights. |
| title | Asymptotically sharp reverse Hölder inequalities for flat Muckenhoupt weights |
| topic | Classical Analysis and ODEs 42B25 (Primary), 42B35 (Secondary) |
| url | https://arxiv.org/abs/1612.01932 |