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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data
Orientation-preserving non-Carleman shift Cauchy singular integral operator
2010/12/14
Suppose is an orientation preserving diffeomorphism (shift)of R+ = (0,∞) onto itself with the only fixed points 0 and ∞. We establish sufficient conditions for the Fredholmness of the singular integ...
New stable numerical solutions of singular integral equations of Abel type by using normalized Bernstein polynomials
Orthonormal Bernstein polynomials Abel’s integral equations
2010/9/10
A new numerical method, based on the normalized Bernstein polynomials for solving singular integral equations of Abel type is presented here in this paper. We construct an othonormal family { }n i n i...
Strongly Singular Integral Operators On Weighted Hardy Space
Strongly singular Calder\'{o}n--Zygmund operatorsStrongly singular Calder\'{o}n--Zygmund operators Hardy spaces $A_p$ weight
2007/12/12
In this paper, we obtain that a strongly singular integral operator is bounded on $L^p_w$ space for $1infty$. We also obtain that a strongly singular integral operator is a bounded operator from $...
Some Maximal Operators related to Singular Integral Operators
Maximal operator Singular Integral Littlewood-Paley Theory Lp€ boundedness
2018/4/20
In this paper, we shall study Lp€boundedness of two kinds of maximal operators related to some families of singular integrals.
Weighted Boundedness for a Rough Homogeneous Singular Integral
Singular integral rough kernel block space weighted norm inequality
2010/2/26
A weighted norm inequality for a homogeneous singular integral with a kernel belonging to a certain block space is proved. Also, some applications of this inequality are obtained. Our results are esse...
Rough Oscillatory Singular Integral Operators-II
Oscillatory singular integral operators Rough kernels Lp estimates Hardy Littlewood maximal function
2010/2/26
In this paper, we study certain classes of oscillatory singular integral operators with kernels in Llog L(Sn-1) which is known to be the most desirable size condition for the Lp boundedness to hold. W...
Lp Boundedness of a Class of Singular Integral Operators with Rough Kernels
Singular integrals oscillatory integrals Fourier transform Lp boundedness rough kernels block spaces
2010/3/1
In this paper, we study the Lp mapping properties of singular integral operators with kernels belonging to certain block spaces. These operators have singularities along sets of the form {x=F (|y|)y'}...