New proofs of two-weight norm inequalities for the maximal operator.
Sharp error bounds for the trapezoidal rule and Simpson's rule.
Corrections to “The maximal function on variable spaces".
The boundedness of classical operators on variable spaces.
The maximal function on variable spaces.
Endpoint estimates and weighted norm inequalities for commutators of fractional integrals.
Weighted Norm Inequalities for Geometric Fractional Maximal Operators.
A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces
We give a new proof using the classic Calderón-Zygmund decomposition that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space whenever the exponent function satisfies log-Hölder continuity conditions. We include the case where assumes the value infinity. The same proof also shows that the fractional maximal operator , , maps into , where .
The fractional maximal operator and fractional integrals on variable spaces.
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