On the boundedness of Cauchy singular operator from the spaceL p toL q ,p>q>-1

G. Khuskivadze; V. Paatashvili

doi:10.1007/bf02307447

On the boundedness of Cauchy singular operator from the spaceL p toL q ,p>q>-1

Georgian Mathematical Journal ◽

10.1007/bf02307447 ◽

1994 ◽

Vol 1 (4) ◽

pp. 395-403

Author(s):

G. Khuskivadze ◽

V. Paatashvili

Keyword(s):

Singular Operator ◽

Cauchy Singular Operator

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Boundedness in Lebesgue Spaces with Variable Exponent of the Cauchy Singular Operator on Carleson Curves

Modern Operator Theory and Applications - Operator Theory: Advances and Applications ◽

10.1007/978-3-7643-7737-3_10 ◽

2007 ◽

pp. 167-186 ◽

Cited By ~ 7

Author(s):

Vakhtang Kokilashvili ◽

Vakhtang Paatashvili ◽

Stefan Samko

Keyword(s):

Variable Exponent ◽

Singular Operator ◽

Lebesgue Spaces ◽

Cauchy Singular Operator

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A criterion for the weighted Cauchy singular operator to belong to the algebra of singular integral operators with coefficients in a Sarason algebra

Functional Analysis and Its Applications ◽

10.1007/bf01076114 ◽

1995 ◽

Vol 28 (4) ◽

pp. 287-288 ◽

Cited By ~ 1

Author(s):

K. A. Georgiev ◽

V. M. Deundyak

Keyword(s):

Singular Integral ◽

Integral Operators ◽

Singular Integral Operators ◽

Singular Operator ◽

Cauchy Singular Operator

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On the Boundedness of Cauchy Singular Operator from the Space Lp to Lq , p > q ≥ 1

Georgian Mathematical Journal ◽

10.1515/gmj.1994.395 ◽

1994 ◽

Vol 1 (4) ◽

pp. 395-403

Author(s):

G. Khuskivadze ◽

C. Paatashvili

Keyword(s):

Lebesgue Space ◽

Singular Operator ◽

Cauchy Type ◽

The Space Lp ◽

Necessary And Sufficient ◽

Cauchy Singular Operator

Abstract It is proved that for a Cauchy type singular operator, given by equality (Khvedelidze, Current problems of mathematics 7: 5-162, 1975), to be bounded from the Lebesgue space Lp (Γ) to Lq (Γ), as , it is necessary and sufficient that either condition (Calderon, Proc. Nat. Acad. Sci. USA 4: 1324-1327, 1977) or (David, L'integrale de Cauchy sur le courbes rectifiables, Prepublications Univ. Paris–Sud; Dept. Math., 1982) be fulfilled.

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Singular Operator as a Parameter of Self-adjoint Extensions

Operator Theory and Related Topics ◽

10.1007/978-3-0348-8413-6_12 ◽

2000 ◽

pp. 205-223 ◽

Cited By ~ 2

Author(s):

Volodymyr Koshmanenko

Keyword(s):

Singular Operator

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A vector p-Laplacian type approach to multiple periodic solutions for the p-relativistic operator

Communications in Contemporary Mathematics ◽

10.1142/s0219199716500292 ◽

2017 ◽

Vol 19 (03) ◽

pp. 1650029 ◽

Cited By ~ 2

Author(s):

Petru Jebelean ◽

Jean Mawhin ◽

Călin Şerban

Keyword(s):

Differential Operator ◽

Periodic Solutions ◽

Differential Inclusions ◽

Singular Operator ◽

Multiple Periodic Solutions ◽

Vector Formula

We prove the existence of at least [Formula: see text] geometrically distinct [Formula: see text]-periodic solutions for a differential inclusions system of the form [Formula: see text] Here, [Formula: see text] is a monotone homeomorphism, [Formula: see text] is periodic with respect to each component of the second variable and [Formula: see text] stands for the generalized Clarke gradient of [Formula: see text] at [Formula: see text]. The monotonicity assumptions on [Formula: see text] highlight the vector [Formula: see text]-Laplacian as being the prototype differential operator. The main interesting feature of this approach is that it also provides a useful framework to treat the case of the [Formula: see text]-relativistic singular operator.

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