Some conjectures aboutL p norms of k-plane transforms |
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Authors: | Albert Baernstein Michael Loss |
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Affiliation: | (1) Mathematics Department, Washington University, 63130 St. Louis, Missouri;(2) School of Mathematics, Georgia Institute of Technology, 30332-0160 Atlanta, GA |
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Abstract: | For 1≤k≤n-1, the k-plane transformT k,n carries functionsf defined onR n to functionsT k,n f defined on the set of affine k-planes inR n . It is known thatT k,n mapsL p intoL q for certain values ofp andq. In this article we formulate conjectures for the exact values of the norm of theT k,n , and state also a conjecture asserting that theL q norm ofT k,n f changes monotonically whenf is replaced by its symmetric decreasing rearrangement. Conferenza tenuta il 6 marzo 1997 The first author was supported in part by NSF grants DMS-9206319 and DMS-9501293. The second author was supported in part by NSF grant DMS-9500840 |
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