Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians |
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Authors: | EB Davies B Simon |
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Institution: | Department of Mathematics, King''s College, Strand, London WC2R 2LS, England;Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125 USA |
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Abstract: | Abstract connections between integral kernels of positivity preserving semigroups and suitable Lp contractivity properties are established. Then these questions are studied for the semigroups generated by , the Dirichlet Laplacian for an open, connected region Ω. As an application under a suitable hypothesis, Sobolev estimates are proved valid up to ?Ω, of the form , where ?0 is the unique positive L2 eigenfunction of . |
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