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 and 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. doi: 10.22075/ijnaa.2012.40
MLA
Daher,R , and 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
R Daher and M El Hamma, "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