广义有界变差函数类的lltpgt连续模估计.docx

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Abstract
The main aim of this dissertation is to ilw∞tig咖estimates of Lp modulus of continuity
As n generalization of the welt-known function of bounded variation,the definition of func- tions of A妒-bounded variation∞mbille8 the notions of fhnction of A-bounded variation and qo-bounded many important classe8 of functions aM special ca%of the c18s8
of functions of A_P-bounded them age cla[Ⅺe$of functions of A-bounded variation,C-bounded variation,肛bounded variation and harmonic bounded variation etc.
lations between oertain cins目of functions and the class H:m the Lipschitz class H:.and,
summability and convergence of trigonometric series depend on esthnates of k modulus of continulty of the corresponding classes of functions in many research topics in Approxinmtion
is of significant importance to estimate Lp modulus of continuity of some important
ela鹤档of functions.
For the case of that妒is convex,we obtain$ome estimates of“modulus of continuity of class of functions of A-bounded variation and-o-bounded variation and its some special c8%.
Our∞tim姻am 8haxp in the sense of ord皤in must cB8峨
As applications ofour characterize 80me觚伍cient and noce88affy conditious ofembedding relationsofAlPBVCH≯(1≤P<∞)and妒Byc月善(1SP<∞).Estimatesof orders of Fourier coefficients of functions of A-bounded variation and妒-bounded variation a∞
and also give the coresponding e8timent8 of that of the results蛳expected to
have applications in trigonometric series and other research fields.
Key words: b modulus of continuity,Generalized bounded variation,A妒一bounded varia- tion,A-bounded variation,妒一bounded variation,Waterman cIa∞,Wiener clag$,Lipschitz class, Embedding,Fourier coefficients.
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