Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909472303087616 |
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| author | Melentijević, Petar |
| author_facet | Melentijević, Petar |
| contents | Let $P_+$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider the inequalities of the following form $$ \|f\|_{L^p(\mathbb{T})}\leq B_{p,s}\|( |P_ + f | ^s + |P_- f |^s) ^{\frac 1s}\|_{L^p (\mathbb{T})} $$ and prove them with sharp constant $B_{p,s}$ for $s \in [p',+\infty)$ and $1<p\leq 2$ and $p\geq 4,$ where $p':=\min\{p,\frac{p}{p-1}\}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections Melentijević, Petar Complex Variables Primary 30H10, 30H05, Secondary 31A05, 31B05 Let $P_+$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider the inequalities of the following form $$ \|f\|_{L^p(\mathbb{T})}\leq B_{p,s}\|( |P_ + f | ^s + |P_- f |^s) ^{\frac 1s}\|_{L^p (\mathbb{T})} $$ and prove them with sharp constant $B_{p,s}$ for $s \in [p',+\infty)$ and $1<p\leq 2$ and $p\geq 4,$ where $p':=\min\{p,\frac{p}{p-1}\}.$ |
| title | Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections |
| topic | Complex Variables Primary 30H10, 30H05, Secondary 31A05, 31B05 |
| url | https://arxiv.org/abs/2408.02453 |