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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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

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

First available in Project Euclid: 31 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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