scholarly journals Boundedness on inhomogeneous Lipschitz spaces of fractional integrals singular integrals and hypersingular integrals associated to non-doubling measures

2009 ◽  
Vol 60 (1) ◽  
pp. 101-114 ◽  
Author(s):  
A. Eduardo Gatto
Keyword(s):  
Singular Integrals ◽  
Fractional Integrals ◽  
Lipschitz Spaces ◽  
Hypersingular Integrals ◽  
Doubling Measures

scholarly journals Numerical methods of computation of singular and hypersingular integrals

2001 ◽  
Vol 28 (3) ◽  
pp. 127-179 ◽  
Author(s):  
I. V. Boikov
Keyword(s):  
Numerical Methods ◽  
Singular Integrals ◽  
Analytical Form ◽  
Approximate Methods ◽  
Hypersingular Integrals ◽  
Fixed Singularity

In solving numerous problems in mathematics, mechanics, physics, and technology one is faced with necessity of calculating different singular integrals. In analytical form calculation of singular integrals is possible only in unusual cases. Therefore approximate methods of singular integrals calculation are an active developing direction of computing in mathematics. This review is devoted to the optimal with respect to accuracy algorithms of the calculation of singular integrals with fixed singularity, Cauchy and Hilbert kernels, polysingular and many-dimensional singular integrals. The isolated section is devoted to the optimal with respect to accuracy algorithms of the calculation of the hypersingular integrals.

A note on fractional integral operators defined by weights and non-doubling measures

2010 ◽  
Vol 106 (2) ◽  
pp. 283 ◽  
Author(s):  
Oscar Blasco ◽  
Vicente Casanova ◽  
Joaquín Motos
Keyword(s):  
Measure Space ◽  
Fractional Integral ◽  
Integral Operators ◽  
Metric Measure Space ◽  
Integral Type ◽  
Lebesgue Spaces ◽  
Lipschitz Spaces ◽  
Fractional Integral Operators ◽  
Doubling Measures

Given a metric measure space $(X,d,\mu)$, a weight $w$ defined on $(0,\infty)$ and a kernel $k_w(x,y)$ satisfying the standard fractional integral type estimates, we study the boundedness of the operators $K_w f(x)=\int_X k_w(x,y)f(y)\,d\mu(y)$ and $\tilde K_w f(x)=\int_X (k_w(x,y)-k_w(x_0,y))f(y)\,d\mu(y)$ on Lebesgue spaces $L^p(\mu)$ and generalized Lipschitz spaces $\mathrm{Lip}_\phi$, respectively, for certain range of the parameters depending on the $n$-dimension of $\mu$ and some indices associated to the weight $w$.

scholarly journals Martingale Morrey-Hardy and Campanato-Hardy Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Eiichi Nakai ◽  
Gaku Sadasue ◽  
Yoshihiro Sawano
Keyword(s):  
Hardy Spaces ◽  
Fractional Integrals ◽  
Lipschitz Spaces

We introduce generalized Morrey-Campanato spaces of martingales, which generalize both martingale Lipschitz spaces introduced by Weisz (1990) and martingale Morrey-Campanato spaces introduced in 2012. We also introduce generalized Morrey-Hardy and Campanato-Hardy spaces of martingales and study Burkholder-type equivalence. We give some results on the boundedness of fractional integrals of martingales on these spaces.

scholarly journals Integro-differential equations with singular and hypersingular integrals

2019 ◽  
Vol 54 (4) ◽  
pp. 404-407 ◽  
Author(s):  
E. I. Zverovich ◽  
A. P. Shilin
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Singular Integrals ◽  
Closed Curve ◽  
Special Structure ◽  
Finite Part ◽  
Hypersingular Integrals ◽  
Hadamard Finite Part

Quadrature linear integro-differential equations on a closed curve located in the complex plane are solved. The equations contain singular integrals which are understood in the sense of the main value and hypersingular integrals which are understood in the sense of the Hadamard finite part. The coefficients of the equations have a special structure.

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