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

Studia Mathematica (1993)

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

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topWheeden, 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

top- [FS] C. L. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. Zbl0222.26019
- [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.
- [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
- [S1] E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11. Zbl0508.42023
- [S2] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345. Zbl0539.42008
- [S3] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545.
- [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
- [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

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

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