Geodesic
$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative
Studia Mathematica, Tome 120 (1996) no. 3, pp. 271-288

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-120-3-271-288
Keywords: Hardy spaces, p-atom, interpolation, Walsh functions, dyadic derivative

Ferenc Weisz 1

1 
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Ferenc Weisz. $(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative. Studia Mathematica, Tome 120 (1996) no. 3, pp. 271-288. doi: 10.4064/sm-120-3-271-288

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