scholarly journals Boundedness of Vector-Valued Intrinsic Square Functions in Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hua Wang
Keyword(s):  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Square Functions ◽  
Doubling Condition ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued ◽  
Intrinsic Square Functions

We will obtain the strong type and weak type estimates for vector-valued analogues of intrinsic square functions in the weighted Morrey spacesLp,κ(w)when1≤p<∞,0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Vector-Valued Inequalities in the Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Hua Wang
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Doubling Condition ◽  
Littlewood Maximal Function ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued

We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spacesLp,κ(w)when1≤p<∞and0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Estimates of Intrinsic Square Functions on Generalized Weighted Morrey Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Guilian Gao ◽  
Xiaomei Wu
Keyword(s):  
Weak Type ◽  
Morrey Spaces ◽  
Strong Type ◽  
Square Functions ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Intrinsic Square Functions

We prove the boundedness of the intrinsic functions on generalized weighted Morrey spacesMp,φ(w), including the strong type estimates and weak type estimates. Moreover, we define thekth-order commutators generated byBMORnfunctions and intrinsic functions, and obtain their strong type estimates onMp,φ(w). In some cases, we improve previous 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