New pointwise bounds by Riesz potential type operators
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910972955852800 |
|---|---|
| author | Hoang, Cong Moen, Kabe Pérez, Carlos |
| author_facet | Hoang, Cong Moen, Kabe Pérez, Carlos |
| contents | We investigate new pointwise bounds for a class of rough integral operators, $T_{Ω,α}$, for a parameter $0<α<n$ that includes classical rough singular integrals of Calderón and Zygmund, rough hypersingular integrals, and rough fractional integral operators. We prove that the rough integral operators are bounded by a sparse potential operator that depends on the size of the symbol $Ω$. As a result of our pointwise inequalities, we obtain several new Sobolev mappings of the form $T_{Ω,α}:\dot W^{1,p}\rightarrow L^q$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09611 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New pointwise bounds by Riesz potential type operators Hoang, Cong Moen, Kabe Pérez, Carlos Classical Analysis and ODEs We investigate new pointwise bounds for a class of rough integral operators, $T_{Ω,α}$, for a parameter $0<α<n$ that includes classical rough singular integrals of Calderón and Zygmund, rough hypersingular integrals, and rough fractional integral operators. We prove that the rough integral operators are bounded by a sparse potential operator that depends on the size of the symbol $Ω$. As a result of our pointwise inequalities, we obtain several new Sobolev mappings of the form $T_{Ω,α}:\dot W^{1,p}\rightarrow L^q$ |
| title | New pointwise bounds by Riesz potential type operators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2401.09611 |