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2000 | 142 | 1 | 7-24
Tytuł artykułu

On sharp reiteration theorems and weighted norm inequalities

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove sharp end forms of Holmstedt's reiteration theorem which are closely connected with a general form of Gehring's Lemma. Reverse type conditions for the Hardy-Littlewood-Pólya order are considered and the maximal elements are shown to satisfy generalized Gehring conditions. The methods we use are elementary and based on variants of reverse Hardy inequalities for monotone functions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
142
Numer
1
Strony
7-24
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-17
poprawiono
2000-02-25
Twórcy
  • Department of Mathematics, University of Zaragoza, 50009 Zaragoza, Spain
autor
  • Department of Mathematics, Florida Atlantic University, Boca Raton, FL 3341, U.S.A.
  • Department of Mathematics, University of Zaragoza, 50009 Zaragoza, Spain
Bibliografia
  • [AM] M. A. Ari no 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.
  • [AKMP] I. U. Asekritova, N. Ya. Krugljak, L. Maligranda and L. E. Persson, Distribution and rearrangement estimates of the maximal function and interpolation, Studia Math. 124 (1997), 107-132.
  • [BMR] J. Bastero, M. Milman and F. Ruiz, On the connection between weighted norm inequalities, commutators and real interpolation, preprint.
  • [BMR1] J. Bastero, M. Milman and F. Ruiz, Reverse Hölder inequalites and interpolation, in: Proc. Haifa Conf. on Interpolation Theory and Related Topics, to appear.
  • [BR] J. Bastero and F. Ruiz, Elementary reverse Hölder type inequalities with application to operator interpolation theory, Proc. Amer. Math. Soc. 124 (1996), 3183-3192.
  • [Be] G. Bennett, Lower bounds for matrices, Linear Algebra Appl. 82 (1986), 81-98.
  • [BS] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988.
  • [BL] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, New York, 1976.
  • [BK] Y. Brudnyĭ and N. Krugljak, Interpolation Functors and Interpolation Spaces, North-Holland, 1991.
  • [Ca] A. P. Calderón, Spaces between $L^1$ and $L^∞$ and the theorem of Marcinkiewicz, Studia Math. 26 (1966), 273-299.
  • [Cw] M. Cwikel, Monotonicity properties of interpolation spaces II, Ark. Mat. 19 (1981), 123-136.
  • [FM] M. Franciosi and G. Moscariello, Higher integrability results, Manuscripta Math. 52 (1985), 151-170.
  • [Ge] F. W. Gehring, The $L^p$ integrability of partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 123-136.
  • [HLP] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, 1952.
  • [Ho] T. Holmstedt, Interpolation of quasi-normed spaces, Math. Scand. 26 (1970), 177-199.
  • [Iw] T. Iwaniec, The Gehring lemma, in: Quasiconformal Mappings and Analysis (Ann Arbor, MI, 1995), Springer, New York, 1998, 181-204.
  • [JM] B. Jawerth and M. Milman, Extrapolation theory with applications, Mem. Amer. Math. Soc. 440 (1991).
  • [MM] M. Mastyło and M. Milman, A new approach to Gehring's Lemma, preprint.
  • [MO] M. Mastyło and V. Ovchinnikov, On the relation between complex and real methods of interpolation, Studia Math. 125 (1997), 201-218.
  • [Mi] M. Milman, A note on Gehring's Lemma, Ann. Acad. Sci. Fenn. Math. 21 (1996), 389-398.
  • [Mi1] M. Milman, A note on reversed Hardy inequalities and Gehring's lemma, Comm. Pure Appl. Math. 50 (1997), 311-315.
  • [Mu1] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
  • [Mu2] B. Muckenhoupt, Hardy's inequalities with weights, Studia Math. 44 (1972), 31-38.
  • [Ni] P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. 132 (1982), 291-330.
  • [Ov] V. I. Ovchinnikov, The method of orbits in interpolation theory, Math. Rep. 1 (1984), 349-515.
  • [Re] P. F. Renaud, A reversed Hardy inequality, Bull. Austral. Math. Soc. 34 (1986), 225-232.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv142i1p7bwm
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