Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1999; 36(5): 855-890

Printed September 1, 1999

Copyright © The Korean Mathematical Society.

Fractional maximal and integral operators on weighted amalgam spaces

Y. Rakotondratsimba

Abstract

Necessary and sufficient conditions on the weight functions
$u(.)$ and $v(.)$ are derived in order that the
fractional maximal operator $M_\alpha$,
$0\le\alpha<1$, is bounded from the weighted amalgam space
$\ell^s(L^p(\Bbb R,v(x)dx))$ into $\ell^r(L^q(\Bbb R,u(x)dx))$ whenever
$1 fractional integral operator $I_\alpha$, $0<\alpha<1$, is also studied.

Keywords: weighted inequalities, fractional maximal operators, fractional integral operators, amalgam spaces

MSC numbers: 42B25

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