caa a22 4500 605525684 CHVBK 20210128100759.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2484-4 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2484-4 Weighted Integrability of Double Series with Respect to Multiplicative Systems [Elektronische Daten] [S. Volosivets, R. Fadeev] 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. Springer Science+Business Media New York, 2015 Volosivets S. Saratov State University, Saratov, Russia aut Fadeev R. Saratov State University, Saratov, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 51-65 1072-3374 209:1<51 2015 209 10958 https://doi.org/10.1007/s10958-015-2484-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2484-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Volosivets S. Saratov State University, Saratov, Russia aut NATIONALLICENCE 700 1- Fadeev R. Saratov State University, Saratov, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/1(2015-08-01), 51-65 1072-3374 209:1<51 2015 209 10958