# Weighted inequalities for square and maximal functions in the plane

Javier Duoandikoetxea; Adela Moyua

Studia Mathematica (1992)

- Volume: 102, Issue: 1, page 39-47
- ISSN: 0039-3223

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topDuoandikoetxea, Javier, and Moyua, Adela. "Weighted inequalities for square and maximal functions in the plane." Studia Mathematica 102.1 (1992): 39-47. <http://eudml.org/doc/215912>.

@article{Duoandikoetxea1992,

abstract = {We prove weighted inequalities for square functions of Littlewood-Paley type defined from a decomposition of the plane into sectors of lacunary aperture and for the maximal function over a lacunary set of directions. Some applications to multiplier theorems are also given.},

author = {Duoandikoetxea, Javier, Moyua, Adela},

journal = {Studia Mathematica},

keywords = {weighted inequalities; square functions of Littlewood-Paley type; maximal function; multiplier theorems},

language = {eng},

number = {1},

pages = {39-47},

title = {Weighted inequalities for square and maximal functions in the plane},

url = {http://eudml.org/doc/215912},

volume = {102},

year = {1992},

}

TY - JOUR

AU - Duoandikoetxea, Javier

AU - Moyua, Adela

TI - Weighted inequalities for square and maximal functions in the plane

JO - Studia Mathematica

PY - 1992

VL - 102

IS - 1

SP - 39

EP - 47

AB - We prove weighted inequalities for square functions of Littlewood-Paley type defined from a decomposition of the plane into sectors of lacunary aperture and for the maximal function over a lacunary set of directions. Some applications to multiplier theorems are also given.

LA - eng

KW - weighted inequalities; square functions of Littlewood-Paley type; maximal function; multiplier theorems

UR - http://eudml.org/doc/215912

ER -

## References

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- [D] J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc., to appear. Zbl0770.42011
- [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam 1985.
- [K] D. Kurtz, Littlewood-Paley and multiplier theorems on weighted ${L}^{p}$ spaces, Trans. Amer. Math. Soc. 259 (1980), 235-254. Zbl0436.42012
- [NSW] A. Nagel, E. Stein and S. Wainger, Differentiation in lacunary directions, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 1060-1062. Zbl0391.42015
- [R] J. L. Rubio de Francia, Factorization theorems and ${A}_{p}$ weights, Amer. J. Math. 106 (1984), 533-547. Zbl0558.42012
- [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970. Zbl0207.13501
- [St] A. M. Stokolos, On certain classes of maximal and multiplier operators, preprint, Warszawa 1987.
- [Wa] D. Watson, Weighted estimates for singular integrals via Fourier transform estimates, Duke Math. J. 60 (1990), 389-399. Zbl0711.42025

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