Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators

Details Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators

2009-03-17

arxiv.org/abs/0903.2921v2

Revista de la Union Matematica Argentina 50 (2009), numero 2, 201-215

Mathematics

Functional Analysis

Scientific paper

Let L be a non-negative, self-adjoint operator on L^2(\Omega), where (\Omega, d \mu) is a space of homogeneous type. Assume that the semigroup {T_t}_{t>0} generated by -L satisfies Gaussian bounds, or more generally Davies-Gaffney estimates. We say that f belongs to the Hardy space H^1_L if the square function S_h f(x)=(\iint_{\Gamma (x)} |t^2 L e^{-t^2 L} f(y)|^2 \frac{d\mu(y)}{\mu (B_d(x,t))} \frac{dt}{t})^{1/2} belongs to L^1(\Omega, d\mu), where \Gamma(x)={(y,t) \in \Omega \times (0,\infty): d(x,y)

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