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Volumn 47, Issue 2, 2003, Pages 311-358

Discretization and anti-discretization of rearrangement-invariant norms

Author keywords

Classical Lorentz space; Discretizing sequence; Duality theorems; Hilbert norm

Indexed keywords


EID: 2442454464     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_47203_02     Document Type: Article
Times cited : (87)

References (34)
  • 1
    • 0001612261 scopus 로고
    • Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions
    • M. A. ARIÑO AND B. MUCKENHOUPT, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320(2) (1990), 727-735.
    • (1990) Trans. Amer. Math. Soc. , vol.320 , Issue.2 , pp. 727-735
    • Ariño, M.A.1    Muckenhoupt, B.2
  • 2
    • 0002574323 scopus 로고    scopus 로고
    • Sharp weighted multidimensional integral inequalities for monotone functions
    • S. BARZA, L.-E. PERSSON AND J. SORIA, Sharp weighted multidimensional integral inequalities for monotone functions, Math. Nachr. 210 (2000), 43-58.
    • (2000) Math. Nachr. , vol.210 , pp. 43-58
    • Barza, S.1    Persson, L.-E.2    Soria, J.3
  • 3
    • 0004008967 scopus 로고
    • Pure and Applied Mathematics, Academic Press, Inc., Boston, MA
    • C. BENNETT AND R. SHARPLEY, "Interpolation of operators", Pure and Applied Mathematics 129, Academic Press, Inc., Boston, MA, 1988.
    • (1988) Interpolation of Operators , vol.129
    • Bennett, C.1    Sharpley, R.2
  • 4
    • 0001647979 scopus 로고
    • Best constants in reversed Hardy's inequalities for quasimonotone functions
    • J. BERGH, V. BURENKOV AND L.-E. PERSSON, Best constants in reversed Hardy's inequalities for quasimonotone functions, Acta Sci. Math. (Szeged) 59(1-2) (1994), 221-239.
    • (1994) Acta Sci. Math. (Szeged) , vol.59 , Issue.1-2 , pp. 221-239
    • Bergh, J.1    Burenkov, V.2    Persson, L.-E.3
  • 5
    • 0004234640 scopus 로고
    • Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin-New York
    • J. BERGH AND J. LÖFSTRÖM, "Interpolation spaces. An introduction", Grundlehren der Mathematischen Wissenschaften 223, Springer-Verlag, Berlin-New York, 1976.
    • (1976) Interpolation Spaces. An Introduction , vol.223
    • Bergh, J.1    Löfström, J.2
  • 8
    • 0000241445 scopus 로고
    • Weighted Lorentz spaces and the Hardy operator
    • M. J. CARRO AND J. SORIA, Weighted Lorentz spaces and the Hardy operator, J. Funct. Anal. 112(2) (1993), 480-494.
    • (1993) J. Funct. Anal. , vol.112 , Issue.2 , pp. 480-494
    • Carro, M.J.1    Soria, J.2
  • 9
    • 0013492730 scopus 로고
    • Boundedness of some integral operators
    • M. J. CARRO AND J. SORIA, Boundedness of some integral operators, Canad. J. Math. 45(6) (1993), 1155-1166.
    • (1993) Canad. J. Math. , vol.45 , Issue.6 , pp. 1155-1166
    • Carro, M.J.1    Soria, J.2
  • 10
    • 0002014888 scopus 로고    scopus 로고
    • The Hardy-Littlewood maximal function and weighted Lorentz spaces
    • M. J. CARRO AND J. SORIA, The Hardy-Littlewood maximal function and weighted Lorentz spaces, J. London Math. Soc. (2) 55(1) (1997), 146-158.
    • (1997) J. London Math. Soc. (2) , vol.55 , Issue.1 , pp. 146-158
    • Carro, M.J.1    Soria, J.2
  • 11
    • 0000026105 scopus 로고    scopus 로고
    • A sharp rearrangement inequality for the fractional maximal operator
    • A. CIANCHI, R. KERMAN, B. OPIC AND L. PICK, A sharp rearrangement inequality for the fractional maximal operator, Studia Math. 138(3) (2000), 277-284.
    • (2000) Studia Math. , vol.138 , Issue.3 , pp. 277-284
    • Cianchi, A.1    Kerman, R.2    Opic, B.3    Pick, L.4
  • 12
    • 0001602502 scopus 로고    scopus 로고
    • Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
    • D. E. EDMUNDS, R. KERMAN AND L. PICK, Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms, J. Funct. Anal. 170(2) (2000), 307-355.
    • (2000) J. Funct. Anal. , vol.170 , Issue.2 , pp. 307-355
    • Edmunds, D.E.1    Kerman, R.2    Pick, L.3
  • 13
    • 0346248160 scopus 로고    scopus 로고
    • Charles University, Faculty of Mathematics and Physics, Preprint No. MATH-KMA-2001/54, Prague, URL address
    • A. GOGATISHVILI, B. OPIC AND L. PICK, Weighted inequalities for Hardy-type operators involving suprema, Charles University, Faculty of Mathematics and Physics, Preprint No. MATH-KMA-2001/54, Prague (2001), 1-24, URL address: http://www.karlin.mff.cuni.cz/~rokyta/preprint/index.php.
    • (2001) Weighted Inequalities for Hardy-type Operators Involving Suprema , pp. 1-24
    • Gogatishvili, A.1    Opic, B.2    Pick, L.3
  • 14
    • 0040196252 scopus 로고
    • Integral inequalities on a cone of functions with monotonicity properties
    • Russian
    • M. L. GOL'DMAN, Integral inequalities on a cone of functions with monotonicity properties, (Russian), Dokl. Akad. Nauk SSSR 320(5) (1991), 1037-1042; translation in Soviet Math. Dokl. 44(2) (1992), 581-587.
    • (1991) Dokl. Akad. Nauk SSSR , vol.320 , Issue.5 , pp. 1037-1042
    • Gol'dman, M.L.1
  • 15
    • 0039804422 scopus 로고
    • translation in
    • M. L. GOL'DMAN, Integral inequalities on a cone of functions with monotonicity properties, (Russian), Dokl. Akad. Nauk SSSR 320(5) (1991), 1037-1042; translation in Soviet Math. Dokl. 44(2) (1992), 581-587.
    • (1992) Soviet Math. Dokl. , vol.44 , Issue.2 , pp. 581-587
  • 16
    • 0040396852 scopus 로고
    • On integral inequalities on the set of functions with some properties of monotonicity
    • (Friedrichroda), Teubner-Texte Math., Teubner, Stuttgart
    • M. L. GOL'DMAN, On integral inequalities on the set of functions with some properties of monotonicity, in: "Function spaces, differential operators and nonlinear analysis" (Friedrichroda, 1992), Teubner-Texte Math. 133, Teubner, Stuttgart, 1993, pp. 274-279.
    • (1992) Function Spaces, Differential Operators and Nonlinear Analysis , vol.133 , pp. 274-279
    • Gol'dman, M.L.1
  • 17
    • 0030490233 scopus 로고    scopus 로고
    • On the principle of duality in Lorentz spaces
    • M. L. GOL'DMAN, H. P. HEINIG AND V. D. STEPANOV, On the principle of duality in Lorentz spaces, Canad. J. Math. 48(5) (1996), 959-979.
    • (1996) Canad. J. Math. , vol.48 , Issue.5 , pp. 959-979
    • Gol'dman, M.L.1    Heinig, H.P.2    Stepanov, V.D.3
  • 19
    • 0000657482 scopus 로고
    • Weighted inequalities for monotone and concave functions
    • H. P. HEINIG AND L. MALIGRANDA, Weighted inequalities for monotone and concave functions, Studia Math. 116(2) (1995), 133-165.
    • (1995) Studia Math. , vol.116 , Issue.2 , pp. 133-165
    • Heinig, H.P.1    Maligranda, L.2
  • 20
    • 2442581898 scopus 로고    scopus 로고
    • Charles University, Faculty of Mathematics and Physics, Preprint No. MATH-KMA-2002/93, Prague, URL address
    • R. KERMAN AND L. PICK, Optimal Sobolev imbedding spaces, Charles University, Faculty of Mathematics and Physics, Preprint No. MATH-KMA-2002/93, Prague (2002), 1-44, URL address: http://www.karlin.mff.cuni.cz/~rokyta/preprint/index.php.
    • (2002) Optimal Sobolev Imbedding Spaces , pp. 1-44
    • Kerman, R.1    Pick, L.2
  • 21
    • 84966258352 scopus 로고
    • Weighted norm inequalities for general operators on monotone functions
    • S. LAI, Weighted norm inequalities for general operators on monotone functions, Trans. Amer. Math. Soc. 340(2) (1993), 811-836.
    • (1993) Trans. Amer. Math. Soc. , vol.340 , Issue.2 , pp. 811-836
    • Lai, S.1
  • 22
    • 84967710384 scopus 로고
    • On the theory of spaces A
    • G. G. LORENTZ, On the theory of spaces A, Pacific J. Math. 1 (1951), 411-429.
    • (1951) Pacific J. Math. , vol.1 , pp. 411-429
    • Lorentz, G.G.1
  • 23
    • 0032056210 scopus 로고    scopus 로고
    • Weighted inequalities for quasi-monotone functions
    • L. MALIGRANDA, Weighted inequalities for quasi-monotone functions, J. London Math. Soc. (2) 57(2) (1998), 363-370.
    • (1998) J. London Math. Soc. (2) , vol.57 , Issue.2 , pp. 363-370
    • Maligranda, L.1
  • 24
    • 0001481360 scopus 로고
    • Weighted norm inequalities for averaging operators of monotone functions
    • C. J. NEUGEBAUER, Weighted norm inequalities for averaging operators of monotone functions, Publ. Mat. 35(2) (1991), 429-447.
    • (1991) Publ. Mat. , vol.35 , Issue.2 , pp. 429-447
    • Neugebauer, C.J.1
  • 25
    • 0003997917 scopus 로고
    • Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow
    • B. OPIC AND A. KUFNER, "Hardy-type inequalities", Pitman Research Notes in Mathematics Series 219, Longman Scientific & Technical, Harlow, 1990.
    • (1990) Hardy-type Inequalities , vol.219
    • Opic, B.1    Kufner, A.2
  • 26
    • 0009270429 scopus 로고
    • Approximation properties of integrable functions on sets of full measure
    • Russian, no. 4
    • K. I. OSKOLKOV, Approximation properties of integrable functions on sets of full measure, (Russian), Mat. Sb. (N.S.) 103(145) (1977), no. 4, 563-589, 631.
    • (1977) Mat. Sb. (N.S.) , vol.103 , Issue.145 , pp. 563-589
    • Oskolkov, K.I.1
  • 27
    • 0000439959 scopus 로고
    • Boundedness of classical operators on classical Lorentz spaces
    • E. SAWYER, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96(2) (1990), 145-158.
    • (1990) Studia Math. , vol.96 , Issue.2 , pp. 145-158
    • Sawyer, E.1
  • 28
    • 0001793288 scopus 로고
    • Spaces defined by the level function and their duals
    • G. SINNAMON, Spaces defined by the level function and their duals, Studia Math. 111(1) (1994), 19-52.
    • (1994) Studia Math. , vol.111 , Issue.1 , pp. 19-52
    • Sinnamon, G.1
  • 29
    • 0030207942 scopus 로고    scopus 로고
    • The weighted Hardy inequality: New proofs and the case p = 1
    • G. SINNAMON AND V. D. STEPANOV, The weighted Hardy inequality: new proofs and the case p = 1, J. London Math. Soc. (2) 54(1) (1996), 89-101.
    • (1996) J. London Math. Soc. (2) , vol.54 , Issue.1 , pp. 89-101
    • Sinnamon, G.1    Stepanov, V.D.2
  • 30
    • 0032380089 scopus 로고    scopus 로고
    • Lorentz spaces of weak-type
    • J. SORIA, Lorentz spaces of weak-type, Quart. J. Math. Oxford Ser. (2) 49(193) (1998), 93-103.
    • (1998) Quart. J. Math. Oxford Ser. (2) , vol.49 , Issue.193 , pp. 93-103
    • Soria, J.1
  • 31
    • 84968507695 scopus 로고
    • The weighted Hardy's inequality for nonincreasing functions
    • V. D. STEPANOV, The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. 338(1) (1993), 173-186.
    • (1993) Trans. Amer. Math. Soc. , vol.338 , Issue.1 , pp. 173-186
    • Stepanov, V.D.1
  • 32
    • 84963057047 scopus 로고
    • Integral operators on the cone of monotone functions
    • V. D. STEPANOV, Integral operators on the cone of monotone functions, J. London Math. Soc. (2) 48(3) (1993), 465-487.
    • (1993) J. London Math. Soc. (2) , vol.48 , Issue.3 , pp. 465-487
    • Stepanov, V.D.1
  • 33
    • 2442596598 scopus 로고
    • Integral operators on the cone of monotone functions and embeddings of Lorentz spaces
    • Russian
    • V. D. STEPANOV, Integral operators on the cone of monotone functions and embeddings of Lorentz spaces, (Russian), Dokl. Akad. Nauk SSSR 317(6) (1991), 1308-1311; translation in Soviet Math. Dokl. 43(2) (1991), 620-623.
    • (1991) Dokl. Akad. Nauk SSSR , vol.317 , Issue.6 , pp. 1308-1311
    • Stepanov, V.D.1
  • 34
    • 0040990895 scopus 로고
    • translation in
    • V. D. STEPANOV, Integral operators on the cone of monotone functions and embeddings of Lorentz spaces, (Russian), Dokl. Akad. Nauk SSSR 317(6) (1991), 1308-1311; translation in Soviet Math. Dokl. 43(2) (1991), 620-623.
    • (1991) Soviet Math. Dokl. , vol.43 , Issue.2 , pp. 620-623


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