Abstract
We give sharp two-sided estimates of the semigroup generated by the fractional Laplacian plus the Hardy potential on , including the case of the critical constant. We use Davies’ method back-to-back with a new method of integral analysis of Duhamel’s formula.
2010 Mathematics Subject Classification:
Disclosure statement
No potential conflict of interest was reported by the authors.
Acknowledgments
We thank Rupert Frank for detailed comments on [Citation23]. We thank Rodrigo Bañuelos, Bartłomiej Dyda, Jerome Goldstein, Martin Hairer, Panki Kim, Giorgio Metafune, Edwin Perkins, and Yuli Semenov for helpful discussions.
Notes
1 Note that the exponent in the definition of f is denoted β in [Citation3, Corollary 6].
2 The trivial factor is missing in [Citation3, Proposition 5].