Bulletin of the Belgian Mathematical Society - Simon Stevin

Improved direct and converse theorems in weighted Lorentz spaces

Ramazan Akgün and Yunus Emre Yıldırır

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Abstract

In the present work we prove the equivalence of the fractional modulus of smoothness to the realization functional and to the Peetre K-functional in weighted Lorentz spaces. Using this equivalence we obtain an improvement of the direct approximation theorem. Furthermore we prove the improved converse theorem in this space.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 2 (2016), 247-262.

Dates
First available in Project Euclid: 31 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1464710117

Digital Object Identifier
doi:10.36045/bbms/1464710117

Mathematical Reviews number (MathSciNet)
MR3507081

Zentralblatt MATH identifier
1342.41020

Subjects
Primary: 41A25: Rate of convergence, degree of approximation 41A27: Inverse theorems 42A10: Trigonometric approximation

Keywords
Fractional modulus of smoothness realization weighted Lorentz spaces Muckenhoupt weight direct and converse theorem

Citation

Akgün, Ramazan; Yıldırır, Yunus Emre. Improved direct and converse theorems in weighted Lorentz spaces. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 2, 247--262. doi:10.36045/bbms/1464710117. https://projecteuclid.org/euclid.bbms/1464710117


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