Characterizations of Weighted BMO Space and Its Application

LetLbe the infinitesimal generator of an analytic semigroup onL2(Rn)with Gaussian kernel bounds, and letL-α/2be the fractional integrals ofLfor0<α<n. Assume thatb→=(b1,b2,…,bm)is a finite family of locally integrable functions; then the multilinear commutators generated byb→andL-α/2are defined byLb→-α/2f=[bm,…,[b2,[b1,L-α/2]],…]f. Assume thatbjbelongs to weighted BMO space,j=1,2,…,m; the authors obtain the boundedness ofLb→-α/2on weighted Morrey spaces. As a special case, whenL=-Δis the Laplacian operator, the authors also obtain the boundedness of the multilinear fractional commutatorIαb→on weighted Morrey spaces. The main results in this paper are substantial improvements and extensions of some known results.

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Weighted BMO and Hankel operators between Bergman spaces

Indiana University Mathematics Journal ◽

10.1512/iumj.2016.65.5882 ◽

2016 ◽

Vol 65 (5) ◽

pp. 1639-1673 ◽

Cited By ~ 10

Author(s):

Jordi Pau ◽

Ruhan Zhao ◽

Kehe Zhu

Keyword(s):

Bergman Spaces ◽

Hankel Operators ◽

Weighted Bmo

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Linear monotone operators and weighted BMO

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1994-1169887-9 ◽

1994 ◽

Vol 120 (3) ◽

pp. 875-875

Author(s):

Qinsheng Lai

Keyword(s):

Monotone Operators ◽

Weighted Bmo

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Well-posedness and blow-up criterion for the Chaplygin gas equations in ℝN

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891619500218 ◽

2019 ◽

Vol 16 (04) ◽

pp. 639-661 ◽

Cited By ~ 1

Author(s):

Zhen Wang ◽

Xinglong Wu

Keyword(s):

Cauchy Problem ◽

Blow Up ◽

Initial Density ◽

Chaplygin Gas ◽

Bmo Space ◽

Well Posedness ◽

Dimension Formula ◽

The Cauchy Problem ◽

Bounded Below ◽

Blow Up Criterion

We establish a well-posedness theory and a blow-up criterion for the Chaplygin gas equations in [Formula: see text] for any dimension [Formula: see text]. First, given [Formula: see text], [Formula: see text], we prove the well-posedness property for solutions [Formula: see text] in the space [Formula: see text] for the Cauchy problem associated with the Chaplygin gas equations, provided the initial density [Formula: see text] is bounded below. We also prove that the solution of the Chaplygin gas equations depends continuously upon its initial data [Formula: see text] in [Formula: see text] if [Formula: see text], and we state a blow-up criterion for the solutions in the classical BMO space. Finally, using Osgood’s modulus of continuity, we establish a refined blow-up criterion of the solutions.

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Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

Journal of Function Spaces ◽

10.1155/2016/8167392 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8

Author(s):

Bijun Ren ◽

Enbin Zhang

Keyword(s):

Morrey Space ◽

Morrey Spaces ◽

Linear Operators ◽

Identity Operator ◽

Zygmund Operator ◽

Weighted Bmo ◽

Weighted Morrey Space ◽

Weighted Morrey Spaces ◽

Bmo Spaces ◽

Toeplitz Type Operator

LetT1be a generalized Calderón-Zygmund operator or±I(the identity operator), letT2andT4be the linear operators, and letT3=±I. Denote the Toeplitz type operator byTb=T1MbIαT2+T3IαMbT4, whereMbf=bfandIαis the fractional integral operator. In this paper, we investigate the boundedness of the operatorTbon weighted Morrey space whenbbelongs to the weighted BMO spaces.

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Weighted inequalities for some integral operators with rough kernels

Open Mathematics ◽

10.2478/s11533-013-0362-1 ◽

2014 ◽

Vol 12 (4) ◽

Cited By ~ 1

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.

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New Weighted Norm Inequalities for Pseudodifferential Operators and Their Commutators

International Journal of Analysis ◽

10.1155/2013/798528 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

The Anh Bui

Keyword(s):

Function Space ◽

Pseudodifferential Operators ◽

Bmo Space ◽

Weighted Norm ◽

Weighted Inequalities ◽

Weighted Norm Inequalities ◽

Norm Inequalities ◽

Bmo Function ◽

New Class ◽

Muckenhoupt Class

This paper is dedicated to study weighted inequalities for pseudodifferential operators with amplitudes and their commutators by using the new class of weights and the new BMO function space BMO∞ which are larger than the Muckenhoupt class of weights and classical BMO space BMO, respectively. The obtained results therefore improve substantially some well-known results.

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