scholarly journals Convergence Almost Everywhere of Non-convolutional Integral Operators in Lebesgue Spaces

2020 ◽  
Vol 8 (6) ◽  
pp. 705-710
Author(s):  
Yakhshiboev M. U.
Keyword(s):  
Integral Operators ◽  
Lebesgue Spaces ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere

scholarly journals A note on maximal singular integrals with rough kernels

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Feng Liu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Maximal Operators ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Homogeneous Mapping ◽  
Recent Developments ◽  
Maximal Singular Integrals ◽  
Maximal Singular Integral

Abstract In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in $H^{1}({\mathrm{S}}^{n-1})$ H 1 ( S n − 1 ) , which complement some recent developments related to rough maximal singular integrals.

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 Strong Law of Large Numbers of the Offspring Empirical Measure for Markov Chains Indexed by Homogeneous Tree

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Huilin Huang
Keyword(s):  
Markov Chains ◽  
Law Of Large Numbers ◽  
Empirical Measure ◽  
Homogeneous Tree ◽  
Almost Everywhere Convergence ◽  
Strong Law ◽  
Convergence Almost Everywhere ◽  
Almost Everywhere ◽  
Large Numbers

We study the limit law of the offspring empirical measure and for Markov chains indexed by homogeneous tree with almost everywhere convergence. Then we prove a Shannon-McMillan theorem with the convergence almost everywhere.

Boundedness of integral operators associated with the Kontorovich–Lebedev transform in the Lebesgue spaces type

2020 ◽  
pp. 2150081
Author(s):  
Anis Kroumi
Keyword(s):  
Riesz Potential ◽  
Integral Operators ◽  
Type Operator ◽  
Maximal Operators ◽  
Lebesgue Spaces ◽  
Potential Type

In this paper, we prove the boundedness for the maximal and fractional maximal operators and Riesz potential-type operator associated with the Kontorovich–Lebedev transform (KL transform)in the [Formula: see text] spaces.

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