## Proceedings of the American Mathematical Society
/ v.127 no.5. 1999, pp.1463-1471

Author :
Chen, Chang-Pao ; Huang, Xin-Rong

Abstract :
We study the double trigonometric series whose coefficients c $_{jk}$ are such that $\sum_{j=-\infty}^{\infty}\sum_{k=-\infty}^{\infty} c_{jk} . Then its rectangular partial sums converge uniformly to some f $\in $ C(T $^{2}$ ). We give sufficient conditions for the Lebesgue integrability of {f(x, y) - f(x, 0) - f(0, y) + f(0, 0)} $\phi $ (x, y), where $\phi $ (x, y) = 1/xy, 1/x, or 1/y. For certain cases, they are also necessary conditions. Our results extend those of Boas and Moricz from the one-dimensional to the two-dimensional series.

Keyword :
Primary 42B99, 42A16

We describe the dynamics of a class of second order periodic differential equations whose mai..

We consider the set of CR functions on a connected tube submanifold of C $^{n}$ satisfying ..

For a general Sturm-Liouville operator with nonnegative coefficients, we obtain two-sided est..

We give an elementary proof of the principle of local reflexivity.

Let A be a TAF-algebra, Z(A) the centre of A, Id(A) the ideal lattice of A, and Mir(A) the sp..

It is shown that if the Banach space operator T has regular norm-sequence, its vector orbits ..

Two properties of subspaces of Banach algebras are introduced. These are closely related to M..

Least-perimeter enclosures of prescribed area on hyperbolic surfaces are characterized.

Suppose that a and b are elements of a complex unital Banach algebra such that the spectra of..

We study the semi-invariants and weights of a group algebra K[G] over a field K of characteri..