scholarly journals The estimates of the Schatten-Neumann norms of one class of integral operators

2021 ◽  
Vol 21 (2) ◽  
pp. 215-230
Author(s):  
E.N. Lomakina ◽  
◽  
M.S. Sarychev ◽  
◽  
◽  
...  
Keyword(s):  
Integral Operator ◽  
Compact Operator ◽  
Integral Operators ◽  
Lorentz Spaces

The article considers an integral operator acting from Lebesque spaces to Lorentz spaces. The conditions are found under which the compact operator belongs to the Shatten-Neumann classes.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

scholarly journals FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES

2009 ◽  
Vol 80 (2) ◽  
pp. 324-334 ◽  
Author(s):  
H. GUNAWAN ◽  
Y. SAWANO ◽  
I. SIHWANINGRUM
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Homogeneous Type ◽  
Fractional Integral Operators

AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

On the p-norm of an Integral Operator in the Half Plane

2013 ◽  
Vol 56 (3) ◽  
pp. 593-601 ◽  
Author(s):  
Congwen Liu ◽  
Lifang Zhou
Keyword(s):  
Integral Operator ◽  
Half Plane ◽  
Integral Operators ◽  
Bergman Projection ◽  
Partial Answer ◽  
Upper Half Plane ◽  
Weighted Bergman Projection

Abstract.We give a partial answer to a conjecture of Dostanić on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane.

scholarly journals A New Version of the Generalized Krätzel-Fox Integral Operators

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 222 ◽  
Author(s):  
Shrideh Al-Omari ◽  
Ghalib Jumah ◽  
Jafar Al-Omari ◽  
Deepali Saxena
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Convolution Theorem ◽  
Fréchet Space ◽  
Frechet Space ◽  
Generalized Convolution ◽  
Real Numbers ◽  
Convolution Products ◽  
Fox’S H Function ◽  
Krätzel Integral

This article deals with some variants of Krätzel integral operators involving Fox’s H-function and their extension to classes of distributions and spaces of Boehmians. For real numbers a and b > 0 , the Fréchet space H a , b of testing functions has been identified as a subspace of certain Boehmian spaces. To establish the Boehmian spaces, two convolution products and some related axioms are established. The generalized variant of the cited Krätzel-Fox integral operator is well defined and is the operator between the Boehmian spaces. A generalized convolution theorem has also been given.

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

scholarly journals The weak-type (1,1) of Fourier integral operators of order –(n–1)/2

2004 ◽  
Vol 76 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Terence Tao
Keyword(s):  
Hardy Space ◽  
Integral Operator ◽  
Weak Type ◽  
Fourier Integral Operator ◽  
Integral Operators ◽  
Fourier Integral ◽  
Fourier Integral Operators ◽  
Main Ideas

AbstractLet T be a Fourier integral operator on Rn of order–(n–1)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H1 to L1. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion.

Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces

2018 ◽  
Vol 30 (4) ◽  
pp. 997-1011 ◽  
Author(s):  
Hongliang Li ◽  
Qinxiu Sun ◽  
Xiao Yu
Keyword(s):  
Banach Spaces ◽  
Measurable Function ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Lorentz Spaces ◽  
Orlicz Functions ◽  
Hardy Type ◽  
Type Integral ◽  
Type Spaces ◽  
Weighted Lorentz Spaces

Abstract Given measurable functions ϕ, ψ on {\mathbb{R}^{+}} and a kernel function {k(x,y)\geq 0} satisfying the Oinarov condition, we study the Hardy operator Kf(x)=\psi(x)\int_{0}^{x}k(x,y)\phi(y)f(y)\,dy,\quad x>0, between Orlicz–Lorentz spaces {\Lambda_{X}^{G}(w)} , where f is a measurable function on {\mathbb{R}^{+}} . We obtain sufficient conditions of boundedness of {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1}}(w_{1})} and {K:\Lambda_{u_{0}}^{G_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{G_{1},\infty}(w_{% 1})} . We also look into boundedness and compactness of {K:\Lambda_{u_{0}}^{p_{0}}(w_{0})\rightarrow\Lambda_{u_{1}}^{p_{1},q_{1}}(w_{1% })} between weighted Lorentz spaces. The function spaces considered here are quasi-Banach spaces rather than Banach spaces. Specializing the weights and the Orlicz functions, we restore the existing results as well as we achieve new results in the new and old settings.

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