In Hilbert space $L^2(\mathbb{R}^n)$, we prove the equivalence between the modulus of smoothness and the $K$-functionals constructed by the Sobolev space corresponding to the Fourier transform. For this purpose, using a spherical mean operator.
Daher, R. & El Hamma, M. (2012). Equivalence of $K$-functionals and modulus of smoothness for Fourier transform. International Journal of Nonlinear Analysis and Applications, 3(2), 38–43. https://doi.org/10.22075/ijnaa.2012.40
MLA
Daher, R., & El Hamma, M. "Equivalence of $K$-functionals and modulus of smoothness for Fourier transform", International Journal of Nonlinear Analysis and Applications, 3, 2, 2012, 38–43. doi: 10.22075/ijnaa.2012.40
HARVARD
Daher, R., & El Hamma, M. (2012). 'Equivalence of $K$-functionals and modulus of smoothness for Fourier transform', International Journal of Nonlinear Analysis and Applications, 3(2), pp. 38–43. doi: 10.22075/ijnaa.2012.40
CHICAGO
Daher, R. & El Hamma, M., "Equivalence of $K$-functionals and modulus of smoothness for Fourier transform." International Journal of Nonlinear Analysis and Applications, 3 2 (2012): 38–43, doi: 10.22075/ijnaa.2012.40
VANCOUVER
Daher R., El Hamma M. Equivalence of $K$-functionals and modulus of smoothness for Fourier transform. IJNAA. 2012;3(2):38–43. doi: 10.22075/ijnaa.2012.40
International Journal of Nonlinear Analysis and Applications