On weighted Dirichlet spaces of monogenic functions in R3

被引：0

作者：

Avetisyan, Karen ^{[1
]}

Guerlebeck, Klaus ^{[2
]}

机构：

[1] Yerevan State Univ, Fac Math & Mech, Alex Manoogian St 1, Yerevan 0025, Armenia

[2] Bauhaus Univ Weimar, Inst Math Phys, Weimar, Germany

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2018年 / 41卷 / 18期

关键词：

Bergman space; Dirichlet space; harmonic conjugates; monogenic function; reduced quaternion; HARMONIC-FUNCTIONS; HARDY-SPACES; MEAN-VALUES;

D O I：

10.1002/mma.5309

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a recent paper of ours, we proved that a special "harmonic conjugation" operator is not bounded in weighted Bergman spaces L-alpha(2) of quaternion-valued functions in the 3D ball. In the present paper, we prove that, in contrast to the Bergman spaces case, the same operator is bounded in weighted Dirichlet spaces D-alpha(2) of quaternion-valued functions in the 3D ball. Furthermore, applying another approach for a construction of harmonic conjugates, we extend the result to weighted Dirichlet spaces D-alpha(p) with 1 < p < infinity

引用

页码：9511 / 9528

页数：18

共 50 条

[1] On strict inclusions of weighted Dirichlet spaces of monogenic functions
Gürlebeck, K
Malonek, HR
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2001, 64 (01) : 33 - 50
[2] Dirichlet and Hardy spaces of harmonic and monogenic functions
Bernstein, S
Gürlebeck, K
Reséndis, LF
Tovar, LM
[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2005, 24 (04): : 763 - 789
[3] On weighted spaces of monogenic quaternion-valued functions
Gürlebeck, K
[J]. CLIFFORD ANALYSIS AND ITS APPLICATIONS, 2001, 25 : 81 - 89
[4] Boundary Behaviour of Functions in Weighted Dirichlet Spaces
Finbarr Holland
J. Brian Twomey
[J]. Computational Methods and Function Theory, 2007, 7 (2) : 361 - 370
[5] On BQ spaces of hyperholomorphic functions and the Bloch space in R3
Gürlebeck, K
Ahmed, AES
[J]. FINITE OR INFINITE DIMENSIONAL COMPLEX ANALYSIS AND APPLICATIONS, 2004, : 269 - 286
[6] On the Stationary Navier Stokes Problem in R3: An Approach in Weighted Sobolev Spaces
Benjemaa, Mondher
Louati, Hela
Meslameni, Mohamed
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (03)
[7] Weighted sobolev spaces for a scalar model of the stationary oseen equations in R3
Amrouche, Cherfi
Razafison, Ulrich
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2007, 9 (02) : 181 - 210
[8] On ψ-hyperholomorphic Functions in R3
Guerlebeck, K.
Nguyen, H. M.
[J]. 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013), 2013, 1558 : 496 - 501
[9] Weighted Dirichlet spaces of harmonic functions on the real hyperbolic ball
Stoll, Manfred
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (01) : 63 - 89
[10] LINEARIZED NAVIER-STOKES EQUATIONS IN R3 : AN APPROACH IN WEIGHTED SOBOLEV SPACES
Amrouche, Cherif
Meslameni, Mohamed
Necasova, Sarka
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2014, 7 (05): : 901 - 916

← 1 2 3 4 5 →