Gaussian estimates of order α and Lp-spectral independence of generators of C0-semigroups II
Shizuo Miyajima, Hisakazu Shindoh · SUT Journal of Mathematics · 2006
Without any assumptions on the space dimension or boundedness of the region, we prove Lp-spectral independence of generators of C0-semigroups estimated by the positive C0-semigroup e−t(−Δ)α(0<α≤1). In particular, if the semigroup is self-adjoint in L2, it is shown that only the estimate by e−t(−Δ)α is sufficient for Lp-spectral independence. The proof depends on the idea of considering the spectra of the operators e−t(−A)β(0<β<1) and applying the spectral independence result of B.A. Barnes for integral operators, where A is the generator of the semigroup in question.