boundedness of analytic families of fractional integrals
Valentina Casarino, Silvia Secco (2008)
Studia Mathematica
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We consider a double analytic family of fractional integrals along the curve , introduced for α = 2 by L. Grafakos in 1993 and defined by , where ψ is a bump function on ℝ supported near the origin, , z,γ ∈ ℂ, Re γ ≥ 0, α ∈ ℝ, α ≥ 2. We determine the set of all (1/p,1/q,Re z) such that maps to boundedly. Our proof is based on product-type kernel arguments. More precisely, we prove that the kernel is a product kernel on ℝ², adapted to the curve ; as a consequence, we show...