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On a Local Mean Oscillation Decomposition [PDF]
, 2012 In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calder\'{o}n-Zygmund singular integral operators $T$. These applications rely on the inequality $M^{\sharp}_{0,s}(Tf)
Poelhuis, Jonathan, Torchinsky, Alberto
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Solutions for singular Volterra integral equations
Electronic Journal of Qualitative Theory of Differential Equations, 2009 We consider the system of Volterra integral equations $$ \begin{array}{l} u_i(t)=\int_{0}^{t}g_i(t,s)[P_i(s,u_1(s),u_2(s),\cdots, u_n(s)) + Q_i(s,u_1(s),u_2(s),\cdots, u_n(s))]ds, t\in [0,T],1\leq i\leq n \end{array} $$ where $T>0$ is fixed and the ...
Patricia J. Y. Wong
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Finite-part singular integral approximations in Hilbert spaces
International Journal of Mathematics and Mathematical Sciences, 2004 Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on ...
E. G. Ladopoulos +2 more
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Multilinear strongly singular integral operators on non-homogeneous metric measure spaces
Journal of Inequalities and Applications, 2022 Let ( X , d , μ ) $(X,d,\mu )$ be a non-homogeneous metric measure space satisfying the geometrically and upper doubling measure conditions. In this paper, the boundedness in Lebesgue spaces for multilinear strongly singular integral operators on non ...
Hailian Wang, Rulong Xie
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Elliptic perturbations for Hammerstein equations with singular nonlinear term
Electronic Journal of Differential Equations, 2006 We consider a singular elliptic perturbation of a Hammerstein integral equation with singular nonlinear term at the origin. The compactness of the solutions to the perturbed problem and, hence, the existence of a positive solution for the ...
Giuseppe Maria Coclite +1 more
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Quantitative Weighted Estimates of the Lq-Type Rough Singular Integral Operator and Its Commutator
MathematicsLet Ω be a homogeneous function of degree zero on Rn, n≥2, integrable and having mean value zero on the unit sphere Sn−1, and let TΩ be the homogeneous convolution singular integral operator with kernel Ω(x)|x|n.
Shuo Wang, Peize Lv, Xiangxing Tao
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Физика волновых процессов и радиотехнические системы, 2019 The singular integral equation of a thin tubular vibrator is considered. This paper analyzed the dependence of the eigenvalues of the integral operator of the singular integral equation on the frequency and geometric dimensions of the vibrator with the ...
D.P. Tabakov, A.G. Mayorov
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MathematicsIn this paper, for a mixed elliptic-hyperbolic type equation with various degeneration orders and singular coefficients, theorems of uniqueness and existence of the solution to the problem with a missing Tricomi condition on boundary characteristic and ...
Assel Makulbay +3 more
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Наука. Инновации. Технологии, 2022 The work out lines a method of constructing an approximate solution of a differential equation of the second order with input data obtained in the experiment (empirical functions).
Igor Eduardovich Naats +2 more
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Potential method in the theory of Moore-Gibson-Thompson thermoporoelasticity
Archives of MechanicsIn the present paper the linear theory of Moore–Gibson–Thompson thermoporoelasticity is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated.
M. Svanadze
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