Geodesic
Weighted integrability of double series with respect to multiplicative systems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 69-87

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

Necessary and sufficient conditions for $L^p$-integrability with power weight of a function $f$ represented by the double series with respect to a multiplicative system with generalized monotone coefficients are obtained. These conditions are given in terms of the coefficients or their second mixed differences. In addition, the integrability of the difference quotient $(f(x,y)-f(x,0)-f(0,y)+f(0,0))/(xy)$ is studied. 
@article{FPM_2013_18_5_a3,
     author = {S. S. Volosivets and R. N. Fadeev},
     title = {Weighted integrability of double series with respect to multiplicative systems},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {69--87},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a3/}
}
TY  - JOUR
AU  - S. S. Volosivets
AU  - R. N. Fadeev
TI  - Weighted integrability of double series with respect to multiplicative systems
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2013
SP  - 69
EP  - 87
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a3/
LA  - ru
ID  - FPM_2013_18_5_a3
ER  - 
%0 Journal Article
%A S. S. Volosivets
%A R. N. Fadeev
%T Weighted integrability of double series with respect to multiplicative systems
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2013
%P 69-87
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a3/
%G ru
%F FPM_2013_18_5_a3
S. S. Volosivets; R. N. Fadeev. Weighted integrability of double series with respect to multiplicative systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 69-87. http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a3/