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Volumn 22, Issue 2, 2006, Pages 455-487

Superposition operators and functions of bounded p-variation

Author keywords

Boundedness of superposition operators; Functions of bounded p variation; Homogeneous and inhomogeneous Besov spaces; Peetre's embedding theorem

Indexed keywords


EID: 33846655069     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/463     Document Type: Article
Times cited : (48)

References (32)
  • 1
    • 0003998728 scopus 로고
    • Nonlinear superposition operators
    • Cambridge Univ. Press, Cambridge
    • APPELL, J. AND ZABREJKO, P. P.: Nonlinear superposition operators. Cambridge Tracts in Mathematics 95. Cambridge Univ. Press, Cambridge, 1990.
    • (1990) Cambridge Tracts in Mathematics , vol.95
    • APPELL, J.1    ZABREJKO, P.P.2
  • 4
    • 0001771613 scopus 로고
    • Réalisations des espaces de Besov homogènes
    • BOURDAUD, G.: Réalisations des espaces de Besov homogènes. Ark. Mat. 26 (1988), no. 1, 41-54.
    • (1988) Ark. Mat , vol.26 , Issue.1 , pp. 41-54
    • BOURDAUD, G.1
  • 5
    • 0002688685 scopus 로고
    • Le calcul fonctionnel dans les espaces de Sobolev
    • BOURDAUD, G.: Le calcul fonctionnel dans les espaces de Sobolev. Invent. Mata. 104 (1991), no. 2, 435-446.
    • (1991) Invent. Mata , vol.104 , Issue.2 , pp. 435-446
    • BOURDAUD, G.1
  • 7
    • 19844373406 scopus 로고    scopus 로고
    • A sharpness result for powers of Besov functions
    • BOURDAUD, G.: A sharpness result for powers of Besov functions. J. Fanct. Spaces Appl. 2 (2004), no. 3, 267-277.
    • (2004) J. Fanct. Spaces Appl , vol.2 , Issue.3 , pp. 267-277
    • BOURDAUD, G.1
  • 8
    • 21844503684 scopus 로고
    • Fonctions qui opèrent sur les espaces de Besov
    • BOURDAUD, G. AND KATEB, M. E. D.: Fonctions qui opèrent sur les espaces de Besov. Math. Ann. 303 (1995), no. 4, 653-675.
    • (1995) Math. Ann , vol.303 , Issue.4 , pp. 653-675
    • BOURDAUD, G.1    KATEB, M.E.D.2
  • 9
    • 0000864209 scopus 로고
    • Fonctions qui opèrent sur les espaces de Sobolev
    • BOURDAUD, G. AND MEYER, Y.: Fonctions qui opèrent sur les espaces de Sobolev. J. Funct. Anal. 97 (1991), no. 2, 351-360.
    • (1991) J. Funct. Anal , vol.97 , Issue.2 , pp. 351-360
    • BOURDAUD, G.1    MEYER, Y.2
  • 10
    • 33846688664 scopus 로고    scopus 로고
    • Le calcul fonctionnel sous-linéaire dans. les espaces de Besov homogènes
    • BOURDAUD, G. AND MEYER, Y.: Le calcul fonctionnel sous-linéaire dans. les espaces de Besov homogènes. Rev. Mat. Iberoamericana 22 (2006), no. 2, 725-746.
    • (2006) Rev. Mat. Iberoamericana , vol.22 , Issue.2 , pp. 725-746
    • BOURDAUD, G.1    MEYER, Y.2
  • 11
    • 0008607529 scopus 로고
    • Variation Totale d'une Fonction
    • Springer, Berlin
    • BRUNEAU, M.: Variation Totale d'une Fonction. Lecture Notes in Mathematics 413. Springer, Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.413
    • BRUNEAU, M.1
  • 13
    • 33744791194 scopus 로고    scopus 로고
    • Characterizations of function spaces of generalised smoothness
    • FARKAS, W. AND LEOPOLD, H.-G.: Characterizations of function spaces of generalised smoothness. Ann. Mat. Pura Appl. 185 (2006), no. 1, 1-62.
    • (2006) Ann. Mat. Pura Appl , vol.185 , Issue.1 , pp. 1-62
    • FARKAS, W.1    LEOPOLD, H.-G.2
  • 14
    • 0003418232 scopus 로고
    • Geometric measure theory
    • Springer, Berlin
    • FEDERER, H.: Geometric measure theory. Classics in Mathematics. Springer, Berlin, 1969.
    • (1969) Classics in Mathematics
    • FEDERER, H.1
  • 15
    • 0002208904 scopus 로고
    • s of Triebel-Lizorkin type: Pointwise multipliers and spaces on domains
    • s of Triebel-Lizorkin type: Pointwise multipliers and spaces on domains. Math. Nachr. 125 (1986), 29-68.
    • (1986) Math. Nachr , vol.125 , pp. 29-68
    • FRANKE, J.1
  • 16
  • 17
    • 0013210680 scopus 로고
    • Imbedding theorems for anisotropic Nikol'skij-Besov spaces with moduli of smoothness of general type
    • GOL'DMAN, M.L.: Imbedding theorems for anisotropic Nikol'skij-Besov spaces with moduli of smoothness of general type. Trudy Mat. Inst. Steklov 170 (1984), 86-104.
    • (1984) Trudy Mat. Inst. Steklov , vol.170 , pp. 86-104
    • GOL'DMAN, M.L.1
  • 19
    • 22844454891 scopus 로고    scopus 로고
    • Fonctions qui opèrent sur les espaces de Besov
    • KATEB, D.: Fonctions qui opèrent sur les espaces de Besov. Proc. Amer. Math. Soc. 128 (2000), no. 3, 735-743.
    • (2000) Proc. Amer. Math. Soc , vol.128 , Issue.3 , pp. 735-743
    • KATEB, D.1
  • 20
    • 0011379845 scopus 로고
    • On a class of functions and their Fourier series
    • MARCINKIEWICZ, J.: On a class of functions and their Fourier series. C.R. Soc. Sci. Varsovie 26 (1934), 71-77.
    • (1934) C.R. Soc. Sci. Varsovie , vol.26 , pp. 71-77
    • MARCINKIEWICZ, J.1
  • 21
    • 0001496464 scopus 로고
    • Every superposition operator mapping one Sobolev space into another is continuous
    • MARCUS, M. AND MIZEL, V.J.: Every superposition operator mapping one Sobolev space into another is continuous. J. Funct. Anal. 33 (1979), 217-229.
    • (1979) J. Funct. Anal , vol.33 , pp. 217-229
    • MARCUS, M.1    MIZEL, V.J.2
  • 22
    • 0002918259 scopus 로고
    • On the boundedness of the mapping f → |f| in Besov spaces
    • OSWALD, P.: On the boundedness of the mapping f → |f| in Besov spaces. Comment. Math. Univ. Carol. 33 (1992), no. 1, 57-66.
    • (1992) Comment. Math. Univ. Carol , vol.33 , Issue.1 , pp. 57-66
    • OSWALD, P.1
  • 23
    • 0002360744 scopus 로고
    • Interpolation of Lipschitz operators and metric spaces
    • PEETRE, J.: Interpolation of Lipschitz operators and metric spaces. Mathematica (Cluj) 12 (1970), 325-334.
    • (1970) Mathematica (Cluj) , vol.12 , pp. 325-334
    • PEETRE, J.1
  • 24
    • 85157226110 scopus 로고    scopus 로고
    • PEETRE, J.: New thoughts on Besov spaces. Duke University Mathematics Series I. Duke University Mathematics Department, Durham, N.C., 1976.
    • PEETRE, J.: New thoughts on Besov spaces. Duke University Mathematics Series I. Duke University Mathematics Department, Durham, N.C., 1976.
  • 25
    • 0003419898 scopus 로고    scopus 로고
    • Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations
    • Walter de Gruyter, Berlin
    • RUNST, T. AND SICKEL, W.: Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations. De Gruyter Series in Nonlinear Analysis and Applications 3. Walter de Gruyter, Berlin, 1996.
    • (1996) De Gruyter Series in Nonlinear Analysis and Applications , vol.3
    • RUNST, T.1    SICKEL, W.2
  • 26
    • 0030295631 scopus 로고    scopus 로고
    • On the regularity of the positive part of functions
    • SAVARÉ, G.: On the regularity of the positive part of functions. Nonlinear Anal. Theory Methods Appl. 27 (1996), no. 9, 1055-1074.
    • (1996) Nonlinear Anal. Theory Methods Appl , vol.27 , Issue.9 , pp. 1055-1074
    • SAVARÉ, G.1
  • 27
    • 0040005840 scopus 로고    scopus 로고
    • Superposition and chain rule for bounded Hessian functions
    • SAVARÉ, G. AND TOMARELLI, F.: Superposition and chain rule for bounded Hessian functions. Adv. Math. 140 (1998), no. 2, 237-281.
    • (1998) Adv. Math , vol.140 , Issue.2 , pp. 237-281
    • SAVARÉ, G.1    TOMARELLI, F.2
  • 30
    • 0004058897 scopus 로고
    • Theory of Function Spaces
    • Birkhäuser, Basel
    • TRIEBEL, H.: Theory of Function Spaces. Monographs in Mathematics 78. Birkhäuser, Basel, 1983.
    • (1983) Monographs in Mathematics , vol.78
    • TRIEBEL, H.1
  • 31
    • 0003216183 scopus 로고
    • Theory of Function Spaces II
    • Birkhäuser, Basel
    • TRIEBEL, H.: Theory of Function Spaces II. Monographs in Mathematics 84. Birkhäuser, Basel, 1992.
    • (1992) Monographs in Mathematics , vol.84
    • TRIEBEL, H.1
  • 32
    • 85171984491 scopus 로고
    • The quadratic variation of a function and its Fourier coefficients
    • WIENER, N.: The quadratic variation of a function and its Fourier coefficients. J. Math. Phys. 3 (1924), 72-94.
    • (1924) J. Math. Phys , vol.3 , pp. 72-94
    • WIENER, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.