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|Paper IPM / M / 16743||
Let X be a metric space with a doubling measure and let L be a nonnegative selfadjoint operator in L2(X) which generates a semigroup e−t L whose kernels pt (x, y), t > 0, satisfy the Gaussian upper bound. Inspired by Fefferman's paper , in this note, we give sufficient conditions for which the square function gL,ψ,α* is unbounded
from Lp(X) to Lp(X) . As an application, we discuss the sharpness of the
exponent of aperture α in the [1, Theorem 1.6].
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