Weighted Integrability of Double Trigonometric Series and of Double Series with Respect to Multiplicative Systems with Coefficients of Class R_0~+BVS~2

摘要

In the present paper, we study problems of weighted integrability of double trigonometric series g(x, y) = ∑_(j=1)~∞ ∑_(k=1)~∞ λ_(jk) sin jx sin ky, (1) f(x, y) = ∑_(j=1)~∞ ∑_(k=1)~∞ λ_(jk) COS jx cos ky (2) and of double series with respect to the Price multiplicative systems [1] h(x, y) = ∑_(j=1)~∞ ∑_(k=1)~∞ λ_(jk) x_j(x)x_k(y), (3) where X_j(x) are functions of the Price system. For the definition of this system, see [1]. We only recall that it is defined by a bounded sequence of positive integers {p_j}_j~∞=1 which is also used to construct the sequence {m_n}_n~∞=0, m_0= 1, m_n = p_1…p_n, n > 1.