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Singular integrals with exponential weights

Authors:	E Prestini

Institution:	Department of Mathematics, University of Rome, Tor Vergata, 00133 Rome, Italy

Abstract:	We study the operators $\begin{equation}\overline{V} f (t)= \frac{1}{w(t)} V(f(r) w(r)) (t) \end{equation}$ where is the Hardy-Littlewood maximal function, the Hilbert transform or Carleson operator. Under suitable conditions on the weight of exponential type, we prove boundedness of $\overline{V}$ from $L^{p}$ spaces, defined on $1, +\infty )$ with respect to the measure $w^{2}(t) dt,$ to $L^{p} + L^{2}, 1 < p\leq 2,$ with the same density measure. These operators, that arise in questions of harmonic analysis on noncompact symmetric spaces, are bounded from $L^{p}$ to $L^{p}, 1 < p < \infty ,$ if and only if .

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