WEIGHTED L~p-INEQUALITIES FOR SHARP-MAXIMAL FUNCTIONS ON METRIC SPACES WITH MEASURES

摘要

For metric spaces (X, d) from a certain class an inequality of the form ‖S_σf‖_(L_v~q(X)) ≤ c‖S_ηf‖_(L_μ~p(X)). is proved for the maximal functions S_ηf(x) = sup 1/(η(t)) f_Bf-P_Bfdμ, where "sup" is taken over all balls B containing the point x ∈ X, P_B : L_(μ,loc)~1 → L_(μ,loc)~1, μ and v are measures over X. Some applications of these inequalities to generalized Sobolev spaces over X are given.