Carleson embeddings for Sobolev spaces via heat equation |
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| Authors: | Jie Xiao |
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| Institution: | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada A1C 5S7 |
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| Abstract: | Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on  subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on  that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space  , p∈1,n) into the Lebesgue space  , q∈(0,∞). |
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| Keywords: | Primary 31 35K 42 46E |
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