Probabilistic Approach to Fractional Integrals and the Hardy-littlewood-sobolev Inequality
نویسنده
چکیده
We give a short summary of Varopoulos’ generalised Hardy-LittlewoodSobolev inequality for self-adjoint C0 semigroups and give a new probabilistic representation of the classical fractional integral operators on Rn as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-LittlewoodSobolev inequality based on Burkholder-Gundy and Doob’s inequalities for martingales. CONTENTS
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تاریخ انتشار 2013