Strong Type Estimation from Weak Type Estimates for Some Integral Operators

2000 ◽  
pp. 25-30 ◽  
Author(s):  
Nobuhiko Fujii
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Strong Type ◽  
Weak Type Estimates

scholarly journals Estimates for Fractional Integral Operators and Linear Commutators on Certain Weighted Amalgam Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-25 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Fractional Integrals ◽  
Gaussian Kernel ◽  
Strong Type ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Kernel Bounds ◽  
Amalgam Spaces

In this paper, we first introduce some new classes of weighted amalgam spaces. Then, we give the weighted strong-type and weak-type estimates for fractional integral operators Iγ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators b,Iγ generated by b and Iγ are established as well. In addition, we are going to study related problems about two-weight, weak-type inequalities for Iγ and b,Iγ on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator Mγ and generalized fractional integrals ℒ−γ/2 in the context of weighted amalgam spaces, where 0<γ<n and L is the infinitesimal generator of an analytic semigroup on L2Rn with Gaussian kernel bounds.

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

Weighted inequalities for some integral operators with rough kernels

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
María Riveros ◽  
Marta Urciuolo
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Degree Zero ◽  
Weighted Inequalities ◽  
Rough Kernels ◽  
Type Estimate ◽  
Dini Condition ◽  
Weighted Bmo ◽  
Weak Type Estimates ◽  
Invertible Matrices

AbstractIn this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

scholarly journals Lp(·)–Lq(·) boundedness of some integral operators obtained by extrapolation techniques

2020 ◽  
Vol 27 (3) ◽  
pp. 479-484 ◽  
Author(s):  
Marta Urciuolo ◽  
Lucas Vallejos
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Weak Type Estimates

AbstractGiven a matrix A such that {A^{M}=I} and {0\leq\alpha<n}, for an exponent p satisfying {p(Ax)=p(x)} for a.e. {x\in\mathbb{R}^{n}}, using extrapolation techniques, we obtain {L^{p(\,\cdot\,)}\rightarrow L^{q(\,\cdot\,)}} boundedness, {\frac{1}{q(\,\cdot\,)}=\frac{1}{p(\,\cdot\,)}-\frac{\alpha}{n}}, and weak type estimates for integral operators of the formT_{\alpha}f(x)=\int\frac{f(y)}{|x-A_{1}y|^{\alpha_{1}}\cdots|x-A_{m}y|^{\alpha% _{m}}}\,dy,where {A_{1},\dots,A_{m}} are different powers of A such that {A_{i}-A_{j}} is invertible for {i\neq j}, {\alpha_{1}+\cdots+\alpha_{m}=n-\alpha}. We give some generalizations of these results.

scholarly journals Boundedness ofθ-Type Calderón–Zygmund Operators and Commutators in the Generalized Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Morrey Space ◽  
Weak Type ◽  
Strong Type ◽  
Type Estimate ◽  
Generalized Morrey Space ◽  
Weighted Morrey Space ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Special Cases ◽  
Type Spaces

We first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space as special cases. Then, we discuss the strong-type and weak-type estimates for a class of Calderón–Zygmund type operatorsTθin these new Morrey type spaces. Furthermore, the strong-type estimate and endpoint estimate of commutators[b,Tθ]formed bybandTθare established. Also, we study related problems about two-weight, weak-type inequalities forTθand[b,Tθ]in the Morrey type spaces and give partial results.

scholarly journals The Boundedness of Intrinsic Square Functions on the Weighted Herz Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Weak Type ◽  
Strong Type ◽  
Herz Spaces ◽  
Square Functions ◽  
Area Integral ◽  
Weak Type Estimates ◽  
Lusin Area Integral ◽  
Intrinsic Square Functions

We will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley𝒢-function, and𝒢λ*-function on the weighted Herz spacesK˙qα,p(w1,w2)(Kqα,p(w1,w2))with general weights.

Sign in / Sign up

Export Citation Format

Share Document