Weighted Dirichlet-type inequalities for Steiner symmetrization

1999 ◽  
Vol 8 (1) ◽  
pp. 15-25 ◽  
Author(s):  
F. Brock
Keyword(s):  
Steiner Symmetrization ◽  
Dirichlet Type

scholarly journals Toeplitz Operators on Dirichlet-Type Space of Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin Xia ◽  
Xiaofeng Wang ◽  
Guangfu Cao
Keyword(s):  
Toeplitz Operator ◽  
Boundary Point ◽  
Toeplitz Operators ◽  
Radial Function ◽  
Type Space ◽  
Dirichlet Type ◽  
Algebraic Properties ◽  
Commuting Problem ◽  
Product Problem ◽  
Dirichlet Type Space

We construct a functionuinL2Bn, dVwhich is unbounded on any neighborhood of each boundary point ofBnsuch that Toeplitz operatorTuis a Schattenp-class0<p<∞operator on Dirichlet-type spaceDBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type spaceDBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the formξkuis studied, wherek ∈ Zn,ξ ∈ ∂Bn, anduis a radial function.

scholarly journals A countable set of directions is sufficient for Steiner symmetrization

2011 ◽  
Vol 47 (4) ◽  
pp. 869-873 ◽  
Author(s):  
Gabriele Bianchi ◽  
Daniel A. Klain ◽  
Erwin Lutwak ◽  
Deane Yang ◽  
Gaoyong Zhang
Keyword(s):  
Steiner Symmetrization
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