WEIGHTED Lp–Lq INEQUALITIES FOR THE FRACTIONAL INTEGRAL OPERATOR WHEN 1<q<p<∞

Yves Rakotondratsimba

doi:10.55937/sut/991985351

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Home > Journals > SUT J. Math. > Volume 34 > Issue 2 > Article

June 1998 WEIGHTED

{L^p}

–

{L^q}

INEQUALITIES FOR THE FRACTIONAL INTEGRAL OPERATOR WHEN

1 < q < p < \infty

Yves Rakotondratsimba

Author Affiliations +

Yves Rakotondratsimba¹
¹Institut polytechnique St Louis, EPMI 13 bd de l’Hautil 95 092 Cergy Pontoise France

SUT J. Math. 34(2): 209-222 (June 1998). DOI: 10.55937/sut/991985351

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Abstract

We find necessary conditions and sufficient conditions on weights $u\left( . \right)$ and $v\left( . \right)$ for which the fractional integral operator ${I_\alpha }$ is bounded from the weighted Lebesgue spaces $L_v^p$ into $L_u^q$ whenever $1 < q < p < \infty$ and $0 < \alpha < n$ . Actually such a boundedness is characterized for a large class of weights.

Acknowledgement

The author is indebted to the referee for valuable comments regarding the first version of this paper.

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Yves Rakotondratsimba. "WEIGHTED ${L^p}$ – ${L^q}$ INEQUALITIES FOR THE FRACTIONAL INTEGRAL OPERATOR WHEN $1 < q < p < \infty$ ." SUT J. Math. 34 (2) 209 - 222, June 1998. https://doi.org/10.55937/sut/991985351