Results 1 to 10 of about 2,481 (254)
The Cauchy Integral Operator on the Predual of a Morrey Space [PDF]
Journal of Inequalities and Applications, 2010 We show that the Cauchy integral operator is bounded from Hp,φ(R1) (the predual of a Morrey space) to hp,φ(R1) (the local version of Hp,φ(R1)). To prove our theorem we will introduce generalized atoms and consider a variant of “
Jianmiao Ruan, Jiecheng Chen
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New refinements of the Cauchy–Bunyakovsky inequality [PDF]
Journal of Inequalities and Applications, 2023 This paper presents new refinements on the integral form of Cauchy–Schwartz inequality known as Cauchy–Bunyakovsky inequality. It is proved that when we possess a weighted sum of a set of Cauchy–Bunyakovsky inequalities, there are two forms of ...
Saeed Montazeri
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On Cauchy's Integral Theorem in the Real Plane [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1939 In a rectangle R let p (x, y) and q (x, y) be two continuous functions, and associate with each rectifiable curve C the number \(J(C) = {{\smallint }_{c}}pdx + qdy\). Under which conditions is J the same for any two coterminal curves in R?
Menger Karl
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On the T(1)-theorem for the Cauchy integral
Arkiv for Matematik, 2000 The author defines a weaker growth condition for the measure \(\mu\) than the standard doubling condition \(\mu (2D)\leq const\times\mu (D)\) for each disc \(D\), and gives an alternative proof, with respect to two recent proofs, of the \(L^2(\mu )\)-boundedness of the Cauchy integral operator, i.e., by the integral \(\int_{C}^{}| f| ^2d\mu\) (\(T(1)-\)
Joan Verdera
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Extensions of the Cauchy–Goursat Integral Theorem
Journal of Mathematical Analysis and Applications, 2008 Abstract It is natural to conjecture that if a function f is continuous on the closed region determined by a rectifiable 1-cycle Γ and complex-differentiable on the open region then ∫ Γ f = 0 . The main result is an extension of the classical Cauchy–Goursat Theorem: the equality conjectured holds (with no boundary condition on f ′
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Uniqueness theorems for Cauchy integrals [PDF]
Publicacions Matemàtiques, 2008 19 ...
Melnikov, Mark +2 more
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HYPERHOLOMORPHIC FUNCTIONS WITH VALUES IN A MODIFIED FORM OF QUATERNIONS
Проблемы анализа, 2020 We give the definition of hyperholomorphic pseudocomplex functions, i. e., functions with values in a special form of quaternions, and propose the necessary variables, functions, and Dirac operators to describe the Cauchy integral theorem and the ...
Ji Eun Kim
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Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations [PDF]
Opuscula Mathematica, 2009 The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A
Milena Netka
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Existence and regularity of solutions for hyperbolic functional differential problems [PDF]
Opuscula Mathematica, 2014 A generalized Cauchy problem for quasilinear hyperbolic functional differential systems is considered. A theorem on the local existence of weak solutions is proved.
Zdzisław Kamont
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Fractal and Fractional, 2023 Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations.
Jia Mu, Zhiyuan Yuan, Yong Zhou
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