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

Abstract

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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.

How to cite

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Duoandikoetxea, 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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  1. [Ca] A. Carbery, Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 157-168. Zbl0607.42009
  2. [CF] A. Córdoba and R. Fefferman, On the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 423-425. Zbl0342.42003
  3. [D] J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc., to appear. Zbl0770.42011
  4. [GR] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland, Amsterdam 1985. 
  5. [K] D. Kurtz, Littlewood-Paley and multiplier theorems on weighted L p spaces, Trans. Amer. Math. Soc. 259 (1980), 235-254. Zbl0436.42012
  6. [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
  7. [R] J. L. Rubio de Francia, Factorization theorems and A p weights, Amer. J. Math. 106 (1984), 533-547. Zbl0558.42012
  8. [S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970. Zbl0207.13501
  9. [St] A. M. Stokolos, On certain classes of maximal and multiplier operators, preprint, Warszawa 1987. 
  10. [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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