Convolution in Weighted Lorentz Spaces of Type Γ - Křepela, Martin (Mathematica Scandinavica, 2016)
We characterize boundedness of the convolution operator between weighted Lorentz spaces Γ^p(v) and Γ^q(w) for the range of parameters p,q[1,∞], or p(0,1) and q{1,∞}, or p=∞ and q(0,1). We provide Young-type convolution inequalities of the form \[ \|f* g\|_Γ^q(w) C \|f\|_Γ^p(v)\|g\|_Y, fΓ^p(v), gY, \] characterizing the optimal rearrangement-invariant space Y for which the inequality is satisfied.