Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of ⨍, $M_{γ}⨍$, by an expression involving the nonincreasing rearrangement of ⨍. This estimate is used to obtain necessary and sufficient conditions for the boundedness of $M_γ$ between classical Lorentz spaces.
Kategorie tematyczne
- 47B38: Operators on function spaces (general)
- 47G10: Integral operators
- 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
- 42B25: Maximal functions, Littlewood-Paley theory
- 26D10: Inequalities involving derivatives and differential and integral operators
Czasopismo
Rocznik
Tom
Numer
Strony
277-284
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-24
poprawiono
2000-01-03
Twórcy
autor
- Istituto di Matematica, Facoltà di Architettura, Università di Firenze, Via dell'Agnolo 14, 50122 Firenze, Italy, cianchi@cesit1.unifi.it
autor
- Department of Mathematics, Brock University, St. Catharines, Ontario, Canada, rkerman@spartan.ac.brocku.ca
autor
- Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, opic@math.cas.cz
autor
- Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic, pick@karlin.mff.cuni.cz
Bibliografia
- [AM] M. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727-735.
- [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Pure Appl. Math. 129, Academic Press, New York, 1988.
- [OK] B. Opic and A. Kufner, Hardy-Type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow 1990.
- [S] E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145-158.
- [T] A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Pure Appl. Math. 123, Academic Press, New York, 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv138i3p277bwm