The d-dimensional classical Hardy spaces H_p (T^d) are introduced and it is shown that the maximal operator of the Riemann sums of a distribution is bounded from H_p(T^d)to L_p(T^2) (d/(d+1)<p≤∞) and is of weak t...The d-dimensional classical Hardy spaces H_p (T^d) are introduced and it is shown that the maximal operator of the Riemann sums of a distribution is bounded from H_p(T^d)to L_p(T^2) (d/(d+1)<p≤∞) and is of weak type (1, 1) provided that the supremum in the maximal operator is taken over a positive cone. The same is proved for the conjugate Riemann sums. As a consequence we obtain that every function f∈L_1(T^d)is a.e. Riemann summable to f, provided again that the limit is taken over a positive cone.展开更多
基金This research was partly supported by the Hungarian Scientific Research Funds (OTKA) No F019633.
文摘The d-dimensional classical Hardy spaces H_p (T^d) are introduced and it is shown that the maximal operator of the Riemann sums of a distribution is bounded from H_p(T^d)to L_p(T^2) (d/(d+1)<p≤∞) and is of weak type (1, 1) provided that the supremum in the maximal operator is taken over a positive cone. The same is proved for the conjugate Riemann sums. As a consequence we obtain that every function f∈L_1(T^d)is a.e. Riemann summable to f, provided again that the limit is taken over a positive cone.
