Plancherel-poLya Inequalities In The Anisotropic Besov Spaces And The Anisotropic Triebel-lizorkin Spaces And Its Application

In this paper, we prove the Plancherel-Polya inequality of the anisotropicBesov space well portrayed by the inequality. We also confirm the Plancherel-Polyainequality of the anisotropic Triebel-Lizorkin space, and use this inequality to give thecharacterization of the anisotropic Triebel-Lizorkin space.There are four chapters in this paper.In the first chapter, we briefly describe the research results of anisotropic spaceof domestic and foreign, some assumptions used in this paper, and the structure of thispaper.In the second chapter, we introduce the notations and related lemmas ofanisotropic Besov spaces and Triebel-Lizorkin spaces.In the third chapter and the fourth chapter, we prove the Plancherel-Polyainequality of the anisotropic Besov space well portrayed by the inequality, and alsoconfirm the inequality of the anisotropic Triebel-Lizorkin space, and use thisinequality to give the characterization of the anisotropic Triebel-Lizorkin space.