Plancherel Type Estimates and Sharp Spectral Multipliers
We study general spectral multiplier theorems for self-adjoint positive definite operators on L2(X, [mu]), where X is any open subset of a space of homogeneous type. We show that the sharp Hörmander-type spectral multiplier theorems follow from the appropriate estimates of the L2 norm of the kernel of spectral multipliers and the Gaussian bounds for the corresponding heat kernel. The sharp Hörmander-type spectral multiplier theorems are motivated and connected with sharp estimates for the...[Show more]
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