Abstract The objective of this work is to prove theorems analogous to Abilov’s theorems in the framework of Clifford algebra analysis. More precisely, we define the moduli of continuity of all orders constructed by the generalized Steklov operator. We give a new version of Abilov’s estimates using in this case the generalized Clifford–Fourier transform in the space L2(R(p,q),Cl(p,q))documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L^{2}({mathbb {R}}^{(p,q)},{mathcal {C}}l_{(p,q)})$$end{document} as applied to some classes of functions characterized by a generalized modulus of continuity.
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