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Paper   IPM / M / 16743
School of Mathematics
  Title:   Comments on "Sharp weighted estimates for square functions associated to operators on spaces of homogeneous type"
  Author(s):  Mahdi Hormozi (Joint with K. Yabuta)
  Status:   To Appear
  Journal: J. Geom. Anal.
  Supported by:  IPM
  Abstract:
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 et L whose kernels pt (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 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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