Geodesic
Multidimensional Fourier transforms on an amalgam type space
Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 63-74

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

Generalizing the known results on the Fourier transforms on an amalgam type space, we introduce a multidimensional analogue of such a space, a subspace of $L^1(\mathbb{R}_+^n)$. Integrability results for the Fourier transforms are obtained provided that certain derivatives of the transformed function are in that space. As an application, we obtain conditions for the integrability of multiple trigonometric series. 
@article{EMJ_2019_10_4_a6,
     author = {E. Liflyand},
     title = {Multidimensional {Fourier} transforms on an amalgam type space},
     journal = {Eurasian mathematical journal},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a6/}
}
TY  - JOUR
AU  - E. Liflyand
TI  - Multidimensional Fourier transforms on an amalgam type space
JO  - Eurasian mathematical journal
PY  - 2019
SP  - 63
EP  - 74
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a6/
LA  - en
ID  - EMJ_2019_10_4_a6
ER  - 
%0 Journal Article
%A E. Liflyand
%T Multidimensional Fourier transforms on an amalgam type space
%J Eurasian mathematical journal
%D 2019
%P 63-74
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a6/
%G en
%F EMJ_2019_10_4_a6
E. Liflyand. Multidimensional Fourier transforms on an amalgam type space. Eurasian mathematical journal, Tome 10 (2019) no. 4, pp. 63-74. http://geodesic.mathdoc.fr/item/EMJ_2019_10_4_a6/