Abstract
Given a space (Ω, d, μ) of homogeneous type, necessary and sufficient conditions are obtained which ensure that given a non-negative weight function U(x) there is a non-negative weight function V(x) which is finite a.e. and the fractional maximal function operator is bounded from Lp(Vdμ) to Lq(Udμ). The dual problem and the analogous problems for non-isotropic fractional integrals are also solved.KeywordsMaximal FunctionFractional IntegralHomogeneous TypeWeight Norm InequalityWeighted InequalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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