Orlicz boundedness for certain classical operators
Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orli...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2002 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/100607 |
| Acesso em linha: | http://hdl.handle.net/11336/100607 |
| Access Level: | acceso abierto |
| Palavra-chave: | BOUNDEDNESS FRACTIONAL INTEGRAL HILBERT TRANSFORM MAXIMAL FUNCTION ORLICZ SPACES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let ɸ and ψ be functions defined on [0,∞) taking the value zero at zero and with non-negative continuous derivative. Under very mild extra assumptions we find necessary and sufficient conditions for the fractional maximal operator M∞Ω, associated to an open bounded set Ω, to be bounded from the Orlicz space Lψ(Ω) into Lɸ(Ω), 0 ≤ α < n. For functions ɸ of finite upper type these results can be extended to the Hilbert transform f on the one-dimensional torus and to the fractional integral operator IαΩ, 0 < α < n. Since these operators are linear and self-adjoint we get, by duality, boundedness results near infinity, deriving in this way some generalized Trudinger type inequalities. |
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