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Caltech/UCLA Joint Analysis Seminar

Tuesday, May 5, 2020
3:00pm to 3:50pm
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Regularity of the centered fractional maximal function
David Beltran, Department of Mathematics, University of Wisconsin-Madison,

I will report some recent progress regarding the boundedness of the map f↦|∇M β f| f↦|∇Mβf| f \mapsto |\nabla M_\beta f| from the endpoint space W 1,1 (R d ) W1,1(Rd) W^{1,1}(\mathbb{R}^d) to L d/(dβ) (R d ) Ld/(d−β)(Rd) L^{d/(d-\beta)}(\mathbb{R}^d) , where M β Mβ M_\beta denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a pointwise relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.

This is joint work with Jose Madrid.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].