FRACTIONAL MAXIMAL AND INTEGRAL OPERATORS ON WEIGHTED AMALGAM SPACES

FRACTIONAL MAXIMAL AND INTEGRAL OPERATORS ON WEIGHTED AMALGAM SPACES

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1<p\leq q<\infty$. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

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