A characterization of some weighted norm inequalities for the fractional maximal function

Richard Wheeden

Studia Mathematica (1993)

  • Volume: 107, Issue: 3, page 257-272
  • ISSN: 0039-3223

Abstract

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A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from L v p ( X ) to L w q ( X ) when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.

How to cite

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Wheeden, Richard. "A characterization of some weighted norm inequalities for the fractional maximal function." Studia Mathematica 107.3 (1993): 257-272. <http://eudml.org/doc/216032>.

@article{Wheeden1993,
abstract = {A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L^p_v(X)$ to $L_w^q(X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.},
author = {Wheeden, Richard},
journal = {Studia Mathematica},
keywords = {weighted norm inequalities; fractional maximal function; homogeneous space},
language = {eng},
number = {3},
pages = {257-272},
title = {A characterization of some weighted norm inequalities for the fractional maximal function},
url = {http://eudml.org/doc/216032},
volume = {107},
year = {1993},
}

TY - JOUR
AU - Wheeden, Richard
TI - A characterization of some weighted norm inequalities for the fractional maximal function
JO - Studia Mathematica
PY - 1993
VL - 107
IS - 3
SP - 257
EP - 272
AB - A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L^p_v(X)$ to $L_w^q(X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.
LA - eng
KW - weighted norm inequalities; fractional maximal function; homogeneous space
UR - http://eudml.org/doc/216032
ER -

References

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  1. [FS] C. L. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. Zbl0222.26019
  2. [GK] M. Gabidzashvili and V. Kokilashvili, Two weight weak type inequalities for fractional-type integrals, preprint, No. 45, Math. Inst. Czech. Acad. Sci., Prague, 1989. 
  3. [P] C. Perez, Two weighted norm inequalities for Riesz potentials and uniform L p -weighted Sobolev inequalities, Indiana Univ. Math. J., 39 (1990), 31-44. Zbl0736.42015
  4. [S1] E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11. Zbl0508.42023
  5. [S2] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345. Zbl0539.42008
  6. [S3] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545. 
  7. [SW1] E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874. Zbl0783.42011
  8. [SW2] E. T. Sawyer and R. L. Wheeden, Carleson conditions for the Poisson integral, Indiana Univ. Math. J. 40 (1991), 639-676. Zbl0748.42009

Citations in EuDML Documents

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  1. Shiying Zhao, On weighted inequalities for operators of potential type
  2. Ana Bernardis, Oscar Salinas, Two-weight norm inequalities for the fractional maximal operator on spaces of homogeneous type
  3. Sérgio Zani, Two-weight norm inequalities for maximal functions on homogeneous spaces and boundary estimates
  4. Toni Heikkinen, Juha Lehrbäck, Juho Nuutinen, Heli Tuominen, Fractional Maximal Functions in Metric Measure Spaces
  5. Bruno Franchi, Guozhen Lu, Richard L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
  6. Wheeden, Richard L., Poincaré–Sobolev and isoperimetric inequalities, maximal functions, and half-space estimates for the gradient

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