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STRONG AND WEAK WEIGHTED NORM INEQUALITIES FOR THE GEOMETRIC FRACTIONAL MAXIMAL OPERATOR

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  30 March 2012

SORINA BARZA  and
CONSTANTIN P. NICULESCU
SORINA BARZA*
Affiliation:
Department of Mathematics, Karlstad University, S-65188 Karlstad, Sweden (email: [email protected])
CONSTANTIN P. NICULESCU
Affiliation:
Department of Mathematics, University of Craiova, Street A.I. Cuza 13, RO-200585 Craiova, Romania (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We characterise the strong- and weak-type boundedness of the geometric fractional maximal operator between weighted Lebesgue spaces in the case 0<p≤q<∞, generalising and improving some older results.

Keywords

geometrical maximal operatorweighted Lebesgue spacestrong-/weak-type inequality

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 205 - 215
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Cruz-Uribe, D., ‘The minimal operator and the geometric maximal operator in ℝn’, Studia Math. 144 (2001), 1–37.CrossRefGoogle Scholar
[2]Cruz-Uribe, D. and Neugebauer, C. J., ‘Weighted norm inequalities for the geometric maximal operator’, Publ. Mat. 42 (1998), 239–263.CrossRefGoogle Scholar
[3]Cruz-Uribe, D., Neugebauer, C. J. and Olesen, V., ‘Weighted norm inequalities for geometric fractional maximal operators’, J. Fourier Anal. Appl. 5 (1999), 45–66.CrossRefGoogle Scholar
[4]Garcia-Cuerva, J. and Martell, J. M., ‘Two-weight norm inequalities for maximal operators and fractional integrals on nonhomogeneous spaces’, Indiana Univ. Math. J. 50 (2001), 1241–1280.CrossRefGoogle Scholar
[5]Grafakos, L., Classical and Modern Fourier Analysis (Pearson Education, Upper Saddle River, NJ, 2004).Google Scholar
[6]Stein, E. M., Singular Integrals and Differentiability Properties of Functions (Princeton University Press, Princeton, NJ, 1970).Google Scholar
[7]Sawyer, E., ‘A characterization of a two-weight norm inequality for maximal operators’, Studia Math. 144 (1982), 1–11.CrossRefGoogle Scholar
[8]Rudin, W., Real and Complex Analysis, 3rd edn (McGraw-Hill, New York–St Louis–San Fransisco, 1986).Google Scholar
[9]Yin, X. and Muckenhoupt, B., ‘Weighted inequalities for the maximal geometric mean operator’, Proc. Amer. Math. Soc. 124 (1996), 75–81.CrossRefGoogle Scholar