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Paper IPM / M / 16743  


Abstract:  
Let X be a metric space with a doubling measure and let L be a nonnegative selfadjoint operator in L^{2}(X) which generates a semigroup e^{−t L} whose kernels p_{t} (x, y), t > 0, satisfy the Gaussian upper bound. Inspired by Fefferman's paper [2], in this note, we give sufficient conditions for which the square function g_{L,ψ,α}^{*} is unbounded
from L^{p}(X) to L^{p}(X) . As an application, we discuss the sharpness of the
exponent of aperture α in the [1, Theorem 1.6].
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