scholarly journals A characterization of internal functions on multiply connected regions

1984 ◽  
Vol 96 ◽  
pp. 23-28
Author(s):  
Lee A. Rubel
Keyword(s):  
Hardy Spaces ◽  
Multiply Connected ◽  
Multiply Connected Regions ◽  
Internal Function

The notion of internal function enters naturally in the study of factorization of function in Lumer’s Hardy spaces—see [RUB], where this aspect is developed in some detail.

Non-tangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators

2015 ◽  
Vol 67 (5) ◽  
pp. 1161-1200 ◽  
Author(s):  
Junqiang Zhang ◽  
Jun Cao ◽  
Renjin Jiang ◽  
Dachun Yang
Keyword(s):  
Hardy Space ◽  
Maximal Function ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic Operator ◽  
Muckenhoupt Class ◽  
Degenerate Elliptic ◽  
Function Characterization

AbstractLet w be either in the Muckenhoupt class of A2(ℝn) weights or in the class of QC(ℝn) weights, and let be the degenerate elliptic operator on the Euclidean space ℝn, n ≥ 2. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space associated with , and when with , the authors prove that the associated Riesz transform is bounded from to the weighted classical Hardy space .

scholarly journals Riesz transform characterization of Hardy spaces associated with certain Laguerre expansions

2010 ◽  
Vol 62 (2) ◽  
pp. 215-231 ◽  
Author(s):  
Jorge Betancor ◽  
Jacek Dziubański ◽  
Gustavo Garrigós
Keyword(s):  
Hardy Spaces ◽  
Riesz Transform ◽  
Laguerre Expansions

scholarly journals Circular Slits Map of Bounded Multiply Connected Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Ali W. K. Sangawi ◽  
Ali H. M. Murid ◽  
M. M. S. Nasser
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Connected Region ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Circular Slit ◽  
Multiply Connected Regions ◽  
Multiply Connected Region

We present a boundary integral equation method for the numerical conformal mapping of bounded multiply connected region onto a circular slit region. The method is based on some uniquely solvable boundary integral equations with adjoint classical, adjoint generalized, and modified Neumann kernels. These boundary integral equations are constructed from a boundary relationship satisfied by a function analytic on a multiply connected region. Some numerical examples are presented to illustrate the efficiency of the presented method.

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