Abstract
Let L be a linear operator defined such that −L generates an associated heat semigroup e−tL. Suppose this semigroup does not satisfy a preservation condition. A proof that a generalised Riesz transform Dg(L) satisfies Lp bounds for some range 2<p<q is provided based on two new estimates. One is a Hardy type inequality for L, the other a bound regarding how the gradient of the heat semigroup acts on a characteristic function. Applications are to cases where L is the Dirichlet Laplacian ΔΩ on inner uniform subsets of Rn.
Original language | English |
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Pages (from-to) | 425-457 |
Number of pages | 33 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 460 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Apr 2018 |
Keywords
- Dirichlet Laplacian
- Harmonic analysis
- Riesz transforms