On some two-dimensional singular integral operators and their applications to elliptic systems of differential equations with singular coefficients

2006 ◽  
Vol 74 (1) ◽  
pp. 577-581
Author(s):  
L. G. Mikhailov ◽  
G. Dzhangibekov ◽  
D. Odinabekov
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Integral Operators ◽  
Elliptic Systems ◽  
Singular Integral Operators ◽  
Two Dimensional ◽  
Systems Of Differential Equations ◽  
Singular Coefficients

The Hardy Space H1 on Manifolds and Submanifolds

1972 ◽  
Vol 24 (5) ◽  
pp. 915-925 ◽  
Author(s):  
Robert S. Strichartz
Keyword(s):  
Partial Differential Equations ◽  
Hardy Space ◽  
Euclidean Space ◽  
Differential Equations ◽  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Riesz Transforms ◽  
Partial Differential ◽  
Integrable Functions

It is well-known that the space L1(Rn) of integrable functions on Euclidean space fails to be preserved by singular integral operators. As a result the rather large Lp theory of partial differential equations also fails for p = 1. Since L1 is such a natural space, many substitute spaces have been considered. One of the most interesting of these is the space we will denote by H1(Rn) of integrable functions whose Riesz transforms are integrable.

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