In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find seve...In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.展开更多
We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. ...We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. for h（t） = log1-Q-c（1/t）. We also discuss how the existence of Lebesgue points follows for u ∈ W1,Q（x） where （X, d, μ） is a complete Q-doubling space supporting a Q-Poincar; inequality for Q 〉 1.展开更多
文摘In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.
基金supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research(Grant No.271983)
文摘We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. for h（t） = log1-Q-c（1/t）. We also discuss how the existence of Lebesgue points follows for u ∈ W1,Q（x） where （X, d, μ） is a complete Q-doubling space supporting a Q-Poincar; inequality for Q 〉 1.
