Quasi–monotone Weight Functions and Their Characteristics and Applications
نویسندگان
چکیده
A weight function w(x) on (0, l) or (l,∞) , is said to be quasi-monotone if w(x)x−a0 C0w(y)y−a0 either for all x y or for all y x, for some a0 ∈ R , C0 1 . In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e.g. in interpolation theory, Fourier analysis, Hardy-type inequalities, singular operators and homogenization theory. Mathematics subject classification (2010): 26A48, 26D10, 26D15.
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