Function spaces as Dirichlet spaces

被引：0
|
作者：
Jacob, N
Schilling, RL
机构：
[1] Univ Coll Swansea, Dept Math, Swansea SA2 8PP, W Glam, Wales
[2] Univ Marburg, FB Math 12, D-35032 Marburg, Germany
来源：
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2005年 / 24卷 / 01期
关键词：
Dirichlet space; anisotropic Sobolev space; Slobodeckij norm; negative definite function; Bernstein function;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
V. G. Maz'ya and J. Nagel found for certain classes of weighted Sobolev norms (defined using the Fourier transform) equivalent Slobodeckij-type difference representations. We extend these considerations to a wider class of anisotropic norms which arise in the theory of Markov processes. In particular we show that these Sobolev norms are equivalent to Dirichlet norms.
引用
收藏
页码：3 / 28
页数：26
相关论文
共 50 条
  • [41] Dirichlet Forms on Noncommutative Spaces
    Cipriani, Fabio
    QUANTUM POTENTIAL THEORY, 2008, 1954 : 161 - 276
  • [42] ON THE REGULARITY OF POTENTIALS OF DIRICHLET SPACES
    MENENDEZ, SC
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1986, 302 (08): : 329 - 331
  • [43] CONTINUITY OF CONTRACTIONS IN DIRICHLET SPACES
    ANCONA, A
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (16): : 871 - 873
  • [44] REGULARIZATION OF DIRICHLET SPACES AND APPLICATIONS
    ALBEVERIO, S
    MA, ZM
    ROCKNER, M
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1992, 314 (11): : 859 - 864
  • [45] Toeplitz operators on Dirichlet spaces
    Lu, YF
    Sun, SH
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2001, 17 (04): : 643 - 648
  • [46] Algebraic Structure on Dirichlet Spaces
    Xing FANG
    Ping HE
    Jian Gang YING
    ActaMathematicaSinica(EnglishSeries), 2006, 22 (03) : 723 - 728
  • [47] Multipliers on Dirichlet Type Spaces
    Hu P.Y.
    Shi J.H.
    Acta Mathematica Sinica, 2001, 17 (2) : 263 - 272
  • [48] On Multipliers of Dirichlet Type Spaces
    Bao, Guanlong
    Lou, Zengjian
    Qian, Ruishen
    Wulan, Hasi
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2015, 9 (08) : 1701 - 1732
  • [49] Toeplitz Algebras on Dirichlet Spaces
    谭艳华
    王晓峰
    Northeastern Mathematical Journal, 2001, (02) : 189 - 194
  • [50] Multipliers between Dirichlet spaces
    Wu, ZJ
    Yang, LM
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 1998, 32 (04) : 482 - 492
12345