Maximal inequalities for square functions and quantitative mean ergodic theorems associated to group metric measure spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914229092614144 |
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| author | Bikram, Panchugopal Saha, Diptesh |
| author_facet | Bikram, Panchugopal Saha, Diptesh |
| contents | In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group metric measure spaces. Then we use these maximal inequalities to prove a quantitative mean ergodic theorem. Our study extends classical harmonic analysis techniques to the non-commutative setting, revealing intricate interactions between group structures, operator-valued functions, and associated filtration systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal inequalities for square functions and quantitative mean ergodic theorems associated to group metric measure spaces Bikram, Panchugopal Saha, Diptesh Functional Analysis Operator Algebras 42B20, 46L52, 46L51, 47A35, 46L55 In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group metric measure spaces. Then we use these maximal inequalities to prove a quantitative mean ergodic theorem. Our study extends classical harmonic analysis techniques to the non-commutative setting, revealing intricate interactions between group structures, operator-valued functions, and associated filtration systems. |
| title | Maximal inequalities for square functions and quantitative mean ergodic theorems associated to group metric measure spaces |
| topic | Functional Analysis Operator Algebras 42B20, 46L52, 46L51, 47A35, 46L55 |
| url | https://arxiv.org/abs/2506.18589 |