Geodesic
Weighted integrability of multiplicative Fourier transforms
Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 71-81

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the relationship between the weighted integrability of a function and that of its multiplicative Fourier transform (MFT). In particular, for the MFT we prove an analog of R. Boas' conjecture related to the Fourier sine and cosine transforms. In addition, we obtain a sufficient condition under which a contraction of an MFT is also an MFT. For the moduli of continuity $\omega$ satisfying N. K. Bari's condition, we present a criterion for determining whether a function with a nonnegative MFT belongs to the class $H^\omega$. 
@article{TRSPY_2010_269_a5,
     author = {S. S. Volosivets and B. I. Golubov},
     title = {Weighted integrability of multiplicative {Fourier} transforms},
     journal = {Informatics and Automation},
     pages = {71--81},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a5/}
}
TY  - JOUR
AU  - S. S. Volosivets
AU  - B. I. Golubov
TI  - Weighted integrability of multiplicative Fourier transforms
JO  - Informatics and Automation
PY  - 2010
SP  - 71
EP  - 81
VL  - 269
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a5/
LA  - ru
ID  - TRSPY_2010_269_a5
ER  - 
%0 Journal Article
%A S. S. Volosivets
%A B. I. Golubov
%T Weighted integrability of multiplicative Fourier transforms
%J Informatics and Automation
%D 2010
%P 71-81
%V 269
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a5/
%G ru
%F TRSPY_2010_269_a5
S. S. Volosivets; B. I. Golubov. Weighted integrability of multiplicative Fourier transforms. Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 71-81. http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a5/