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( H p , L p ) -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space H p , q to L p , q (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type ( L 1 , L 1 ) . As a consequence we show that the dyadic integral of a ∞ function f ∈ L 1 is dyadically differentiable and its derivative is f a.e.

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