A+ CATEGORY SCIENTIFIC UNIT

Orlicz boundedness for certain classical operators

Volume 91 / 2002

E. Harboure, O. Salinas, B. Viviani Colloquium Mathematicum 91 (2002), 263-282 MSC: Primary 42B25; Secondary 46E30. DOI: 10.4064/cm91-2-6

Abstract

Let $\phi $ and $\psi $ be functions defined on $[ 0,\infty ) $ 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 $M_{{\mit \Omega }}^{\alpha }$, associated to an open bounded set ${\mit \Omega } $, to be bounded from the Orlicz space $L^{\psi }({\mit \Omega } )$ into $L^{\phi }({\mit \Omega })$, $0\leq \alpha < n$. For functions $\phi $ of finite upper type these results can be extended to the Hilbert transform $\widetilde {f}$ on the one-dimensional torus and to the fractional integral operator $I_{{\mit \Omega } }^{\alpha }$, $0<\alpha < n$. 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.

Authors

  • E. HarboureInstituto de Matemática Aplicada del Litoral
    Universidad Nacional del Litoral
    Güemes 3450
    3000 Santa Fe, Argentina
    e-mail
  • O. SalinasInstituto de Matemática Aplicada del Litoral
    Universidad Nacional del Litoral
    Güemes 3450
    3000 Santa Fe, Argentina
    e-mail
  • B. VivianiInstituto de Matemática Aplicada del Litoral
    Universidad Nacional del Litoral
    Güemes 3450
    3000 Santa Fe, Argentina
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image