메뉴 건너뛰기




Volumn 19, Issue 1, 2012, Pages 1-22

Convergence in variation for a homothetic modulus of smoothness in multidimensional setting

Author keywords

absolute continuity; modulus of smoothness; Multidimensional variation

Indexed keywords


EID: 84858829075     PISSN: 1074133X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (8)

References (36)
  • 1
    • 84858825582 scopus 로고    scopus 로고
    • A characterization of a modulus of smoothness in multidimensional setting
    • L. Angeloni, A characterization of a modulus of smoothness in multidimensional setting, Bollettino dell'Unione Matematica Italiana, Serie IX, 4 (1) (2011), 79-108.
    • (2011) Bollettino dell'Unione Matematica Italiana, Serie IX , vol.4 , Issue.1 , pp. 79-108
    • Angeloni, L.1
  • 2
    • 33750906082 scopus 로고    scopus 로고
    • Convergence in variation and rate of approximation for nonlinear integral operators of convolution type
    • DOI 10.1007/s00025-006-0208-2
    • L. Angeloni and G. Vinti, Convergence in Variation and Rate of Approximation for Nonlinear Integral Operators of Convolution Type, Results Math., 49(1-2) (2006), 1-23. Erratum: 57 (2010), 387-391. (Pubitemid 44727074)
    • (2006) Results in Mathematics , vol.49 , Issue.1-2 , pp. 1-23
    • Angeloni, L.1    Vinti, G.2
  • 3
    • 53249145747 scopus 로고    scopus 로고
    • Approximation by means of nonlinear integral operators in the space of functions with bounded ψ-variation
    • Erratum: 23(7-8) (2010), 795-799
    • L. Angeloni and G. Vinti, Approximation by means of nonlinear integral operators in the space of functions with bounded ψ-variation, Differential Integral Equations, 20(3) (2007), 339-360. Erratum: 23(7-8) (2010), 795-799.
    • (2007) Differential Integral Equations , vol.20 , Issue.3 , pp. 339-360
    • Angeloni, L.1    Vinti, G.2
  • 4
    • 53249130636 scopus 로고    scopus 로고
    • ψ- spaces in multidimensional setting
    • L. Angeloni and G. Vinti, Convergence and rate of approximation for linear integral operators in BVV- spaces in multidimensional setting, J. Math. Anal. Appl, 349 (2009), 317-334.
    • (2009) J. Math. Anal. Appl , vol.349 , pp. 317-334
    • Angeloni, L.1    Vinti, G.2
  • 5
    • 77954589773 scopus 로고    scopus 로고
    • Approximation with respect to Goffman-Serrin variation by means of non-convolution type integral operators
    • L. Angeloni and G. Vinti, Approximation with respect to Goffman-Serrin variation by means of non-convolution type integral operators, Numer. Funct. Anal. Optim., 31 (2010), 519-548.
    • (2010) Numer. Funct. Anal. Optim. , vol.31 , pp. 519-548
    • Angeloni, L.1    Vinti, G.2
  • 6
    • 29944433767 scopus 로고    scopus 로고
    • Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals
    • C. Bardaro, P.L. Butzer, R.L. Stens, and G. Vinti, Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals, Analysis, 23 (2003), 299-340.
    • (2003) Analysis , vol.23 , pp. 299-340
    • Bardaro, C.1    Butzer, P.L.2    Stens, R.L.3    Vinti, G.4
  • 9
    • 10844258648 scopus 로고
    • On convergence of moment operators with respect to ψ-variation
    • C. Bardaro and G. Vinti, On convergence of moment operators with respect to ψ-variation, Appl. Anal, (1991), 247-256.
    • (1991) Appl. Anal , pp. 247-256
    • Bardaro, C.1    Vinti, G.2
  • 11
    • 84960563638 scopus 로고
    • Functions of intervals
    • J.C. Burkill, Functions of intervals, Proc. London Math. Soc, 22 (1923), 275-310.
    • (1923) Proc. London Math. Soc , vol.22 , pp. 275-310
    • Burkill, J.C.1
  • 13
    • 0000923872 scopus 로고
    • Sulle funzioni a variazione limitata
    • L. Cesari, Sulle funzioni a variazione limitata, Ann. Scuola Norm. Sup. Pisa, 5 (1936), 299-313.
    • (1936) Ann. Scuola Norm. Sup. Pisa , vol.5 , pp. 299-313
    • Cesari, L.1
  • 14
    • 0032050010 scopus 로고    scopus 로고
    • Mappings of bounded φ-variation with arbitrary function φ
    • V. V. Chistyakov and O. E. Galkin, Mappings of Bounded Φ-Variation with Arbitrary Function Φ, J. Dynam. Control Systems, 4(2) (1998), 217-247. (Pubitemid 128514416)
    • (1998) Journal of Dynamical and Control Systems , vol.4 , Issue.2 , pp. 217-247
    • Chistyakov, V.V.1    Galkin, O.E.2
  • 15
    • 0000245505 scopus 로고
    • Su una teoria generale della misura (r-1)-dimensionale in uno spazio ad r dimensioni
    • E. De Giorgi, Su una teoria generale della misura (r-1)-dimensionale in uno spazio ad r dimensioni, Ann. Mat. Pura Appl, 36(4) (1954), 191-213.
    • (1954) Ann. Mat. Pura Appl , vol.36 , Issue.4 , pp. 191-213
    • De Giorgi, E.1
  • 16
    • 0003343498 scopus 로고
    • Minimal surfaces and functions of bounded variation
    • Birkḧauser, Verlag, Basel
    • E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkḧauser Verlag, Basel, 1984.
    • (1984) Monographs in Mathematics , vol.80
    • Giusti, E.1
  • 17
    • 53249149608 scopus 로고
    • Modular spaces of generalized variation
    • H. H. Herda, Modular spaces of generalized variation, Studia Math., 30 (1968), 21-42.
    • (1968) Studia Math. , vol.30 , pp. 21-42
    • Herda, H.H.1
  • 18
    • 0001048449 scopus 로고
    • Sur la serie de Fourier
    • C. Jordan, Sur la serie de Fourier, C. R. Acad. Sci. Paris, 92 (1881), 228-230.
    • (1881) C. R. Acad. Sci. Paris , vol.92 , pp. 228-230
    • Jordan, C.1
  • 19
    • 0346125681 scopus 로고
    • Sur une classe de fonctionnelles lińeaires
    • E. R. Love and L. C. Young, Sur une classe de fonctionnelles lińeaires, Fund. Math., 28 (1937), 243-257.
    • (1937) Fund. Math. , vol.28 , pp. 243-257
    • Love, E.R.1    Young, L.C.2
  • 20
    • 0013097619 scopus 로고
    • On some properties of functions of generalized variation
    • L. Maligranda and W. Orlicz, On some properties of functions of generalized variation, Mh. Math., 104 (1987), 53-65.
    • (1987) Mh. Math. , vol.104 , pp. 53-65
    • Maligranda, L.1    Orlicz, W.2
  • 21
    • 33750925753 scopus 로고    scopus 로고
    • Φ-variation and nonlinear integral operators
    • a special issue of the International Conference in Honour of Prof. Calogero Vinti
    • I. Mantellini and G. Vinti, Φ-variation and nonlinear integral operators, Atti Sem. Mat. Fis. Univ. Modena, Suppl. Vol. 46, a special issue of the International Conference in Honour of Prof. Calogero Vinti (1998), 847-862.
    • (1998) Atti Sem. Mat. Fis. Univ. Modena, Suppl. , vol.46 , pp. 847-862
    • Mantellini, I.1    Vinti, G.2
  • 23
    • 0003311060 scopus 로고
    • Orlicz spaces and modular spaces
    • Springer-Verlag
    • J. Musielak, Orlicz Spaces and Modular Spaces, Springer-Verlag, Lecture Notes in Math., 1034, 1983.
    • (1983) Lecture Notes in Math. , vol.1034
    • Musielak, J.1
  • 24
    • 0042200370 scopus 로고
    • Nonlinear approximation in some modular function spaces i
    • J. Musielak, Nonlinear approximation in some modular function spaces I, Math. Japon., 38 (1993), 83-90.
    • (1993) Math. Japon. , vol.38 , pp. 83-90
    • Musielak, J.1
  • 25
    • 0001845851 scopus 로고
    • On generalized variations (I)
    • J. Musielak and W. Orlicz, On generalized variations (I), Studia Math., 18 (1959), 11-41.
    • (1959) Studia Math. , vol.18 , pp. 11-41
    • Musielak, J.1    Orlicz, W.2
  • 27
    • 34249769183 scopus 로고
    • On approximation of functions in terms of Φ-variation
    • A. R. K. Ramazanov, On approximation of functions in terms of Φ-variation, Anal. Math., 20 (1994), 263-281.
    • (1994) Anal. Math. , vol.20 , pp. 263-281
    • Ramazanov, A.R.K.1
  • 28
    • 10844271189 scopus 로고    scopus 로고
    • ψ for a class of integral operators
    • S. Sciamannini and G. Vinti, Convergence and rate of approximation in BVV for a class of integral operators, Approx. Theory Appl., 17 (2001), 17-35.
    • (2001) Approx. Theory Appl. , vol.17 , pp. 17-35
    • Sciamannini, S.1    Vinti, G.2
  • 29
    • 33750908784 scopus 로고    scopus 로고
    • ψ for a class of nonlinear Volterra-Hammerstein integral operators and applications
    • S. Sciamannini and G. Vinti, Convergence results in BVV for a class of nonlinear Volterra-Hammerstein integral operators and applications, J. Concrete Appl. Anal., 1(4) (2003), 287-306.
    • (2003) J. Concrete Appl. Anal. , vol.1 , Issue.4 , pp. 287-306
    • Sciamannini, S.1    Vinti, G.2
  • 30
    • 53249111792 scopus 로고
    • On convergence of singular integrals in the generalized variation metric
    • J. Szelmeczka, On convergence of singular integrals in the generalized variation metric, Funct. Approx. Comment. Math., 15 (1986), 53-58.
    • (1986) Funct. Approx. Comment. Math. , vol.15 , pp. 53-58
    • Szelmeczka, J.1
  • 31
    • 33750921310 scopus 로고
    • Su alcuni concetti dell'analisi moderna
    • L. Tonelli, Su alcuni concetti dell'analisi moderna, Ann. Scuola Norm. Super. Pisa, 11(2) (1942), 107-118.
    • (1942) Ann. Scuola Norm. Super. Pisa , vol.11 , Issue.2 , pp. 107-118
    • Tonelli, L.1
  • 32
    • 33750918532 scopus 로고
    • Perimetro-variazione
    • C. Vinti, Perimetro-variazione, Ann. Scuola Norm. Sup. Pisa, 18(3) (1964), 201-231.
    • (1964) Ann. Scuola Norm. Sup. Pisa , vol.18 , Issue.3 , pp. 201-231
    • Vinti, C.1
  • 33
    • 84858830165 scopus 로고
    • L'integrale di Fubini-Tonelli nel senso di Weierstrass, I -Caso parametrico
    • C. Vinti, L'integrale di Fubini-Tonelli nel senso di Weierstrass, I -Caso parametrico, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 229-263.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 229-263
    • Vinti, C.1
  • 34
    • 85171984491 scopus 로고
    • The quadratic variation of a function and its Fourier coefficients
    • N. Wiener, The quadratic variation of a function and its Fourier coefficients, Massachusetts J. of Math., 3 (1924), 72-94.
    • (1924) Massachusetts J. of Math. , vol.3 , pp. 72-94
    • Wiener, N.1
  • 35
    • 0000821514 scopus 로고
    • An inequality of the Holder type, connected with Stieltjes integration
    • L. C. Young, An inequality of the Holder type, connected with Stieltjes integration, Acta Math., 67 (1936), 251-282.
    • (1936) Acta Math. , vol.67 , pp. 251-282
    • Young, L.C.1
  • 36
    • 0001018757 scopus 로고
    • ieme borńee au sens de M. Wiener, et sur la convergence des śeries de Fourier
    • L. C. Young, Sur une ǵeńeralisation de la notion de variation de puissance pieme borńee au sens de M. Wiener, et sur la convergence des śeries de Fourier, C. R. Acad. Sci. Paris, 204 (1937), 470-472.
    • (1937) C. R. Acad. Sci. Paris , vol.204 , pp. 470-472
    • Young, L.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.