Symmetric Decreasing Rearrangement Is Sometimes Continuous
نویسندگان
چکیده
This paper deals with the operation .9R 'of symmetric decreasing re-arrangement which maps Wl,p (Rn) to Wi ,p (Rn) . We show that even thoughit is norm decreasing, .9R is not continuous for n ~ 2. The functions at which.9R is continuous are precisely characterized by a new property called co-arearegularity. Every sufficiently differentiable function is co-area regular, and boththe regular and the irregular functions are dense in Wi ,P(Rn ). Curiously, .9Ris always continuous in fractional Sobolev spaces W'" P (Rn) with 0 < a < I . DEPARTMENT OF MATHEMATICS, PRINCETON UNIVERSITY, PRINCETON, NEW JERSEY 08544 License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
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