Ultracontractivity and the Heat Kernel for Schrijdinger Operators and Dirichlet Laplacians
نویسنده
چکیده
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 -A + V and H,, the Dirichlet Laplacian for an open, connected region Q. As an application under a suitable hypothesis, Sobolev estimates are proved valid up to 352, of the form /n(x)1 ,< coo(x) lJHk,nllZ, where o0 is the unique positive L2 eigenfunction of H, .
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