Abstract
One-weight inequalities with general weights for Riemann-Liouville transform andn-dimensional fractional integral operator in variable exponent Lebesgue spaces defined onRnare investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions inLp(x)spaces.
Highlights
We derive necessary and sufficient conditions governing the one-weight inequality for the Riemann-Liouville operator Rαf (x) = 1 xα x ∫ (x f −(t) t)1−α dt 0
One-weight inequalities with general weights for Riemann-Liouville transform and n-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on Rn are investigated
Weighted problems for the Riemann-Liouville transform in Lp(x) spaces were explored in the papers [5, 14,15,16]
Summary
One-weight inequalities with general weights for Riemann-Liouville transform and n-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on Rn are investigated. We derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in Lp(x) spaces. We derive necessary and sufficient conditions governing the one-weight inequality for the Riemann-Liouville operator
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