# $({H}_{p},{L}_{p})$-type inequalities for the two-dimensional dyadic derivative

Studia Mathematica (1996)

- Volume: 120, Issue: 3, page 271-288
- ISSN: 0039-3223

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topWeisz, Ferenc. "$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative." Studia Mathematica 120.3 (1996): 271-288. <http://eudml.org/doc/216337>.

@article{Weisz1996,

abstract = {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.},

author = {Weisz, Ferenc},

journal = {Studia Mathematica},

keywords = {Hardy spaces; p-atom; interpolation; Walsh functions; dyadic derivative; multiple Walsh series; dyadic antiderivative; dyadic finite differences; maximal operator; Hardy-Lorentz spaces},

language = {eng},

number = {3},

pages = {271-288},

title = {$(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative},

url = {http://eudml.org/doc/216337},

volume = {120},

year = {1996},

}

TY - JOUR

AU - Weisz, Ferenc

TI - $(H_p,L_p)$-type inequalities for the two-dimensional dyadic derivative

JO - Studia Mathematica

PY - 1996

VL - 120

IS - 3

SP - 271

EP - 288

AB - 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.

LA - eng

KW - Hardy spaces; p-atom; interpolation; Walsh functions; dyadic derivative; multiple Walsh series; dyadic antiderivative; dyadic finite differences; maximal operator; Hardy-Lorentz spaces

UR - http://eudml.org/doc/216337

ER -

## References

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