Estimates of functionals by generalized moduli of continuity generated by the Dunkl operators

DOI10.1007/s10958-012-0867-3zbMath1267.42008OpenAlexW2091269208MaRDI QIDQ690796

O. L. Vinogradov

Publication date: 29 November 2012

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-0867-3

zbMATH Keywords

Lebesgue spacemomentmodulus of continuityDunkl operatorgeneralized translation operatorgeneralized Sobolev class

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Linear operators on function spaces (general) (47B38) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items

Discrete Jacobi-Dunkl transform and approximation theorems ⋮ On the constants in abstract inverse theorems of approximation theory ⋮ Some direct and inverse theorems of approximation of functions in Jacobi-Dunkl discrete harmonic analysis ⋮ Estimates of functionals by deviations of Steklov type averages generated by Dunkl type operators

Cites Work

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• Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means
• Combinations of multivariate averages
• Equivalence of \(K\)-functionals and modulus of smoothness constructed by generalized Dunkl translations
• Bohr-Favard inequality for functions on compact symmetric spaces of rank one
• Calderon's reproducing formula related to the Dunkl operator on the real line
• On the exact constant in the Jackson-Stechkin inequality for the uniform metric
• Equiconvergence theorems for Chébli-Trimèche hypergroups
• On the Bernstein-Nikol'skii and Favard inequalities on compact homogeneous spaces of rank 1
• Differential-Difference Operators Associated to Reflection Groups
• ON APPROXIMATION OF FUNCTIONS ON THE SPHERE
• Transmutation operators associated with a dunkl type differential-difference operator on the real line and certain of their applications
• A positive radial product formula for the Dunkl kernel
• Sharp Jackson-type inequalities for approximations of classes of convolutions by entire functions of exponential type
• APPROXIMATION OF FUNCTIONS ON THE SPHERE