The inequality (Formula presented) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space Hp on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in Lp whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier series of an arbitrary function from H1 converges a.e. and also in L1 norm to that function.
- Atomic decomposition
- Hardy spaces
- Hardy-Littlewood inequalities
- Rectangle p-atom
ASJC Scopus subject areas