scholarly journals Boundedness of higher order Riesz transforms associated with Schrodinger type operator on generalized Morrey spaces

2017 ◽  
Vol 10 (05) ◽  
pp. 2757-2766 ◽  
Author(s):  
Bijun Ren ◽  
Hui Wang
Keyword(s):  
Morrey Spaces ◽  
Higher Order ◽  
Riesz Transforms ◽  
Type Operator ◽  
Generalized Morrey Spaces ◽  
Schrödinger Type Operator

scholarly journals Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials

2013 ◽  
Vol 2013 ◽  
pp. 1-22
Author(s):  
Pengtao Li ◽  
Qixiang Yang ◽  
Yueping Zhu
Keyword(s):  
Morrey Spaces ◽  
Type Operator ◽  
Inclusion Relation ◽  
Multiplier Space ◽  
Schrödinger Type Operator ◽  
Meyer Wavelets ◽  
Schrödinger Type Operators

We employ Meyer wavelets to characterize multiplier spaceXr,pt(ℝn)without using capacity. Further, we introduce logarithmic Morrey spacesMr,pt,τ(ℝn)to establish the inclusion relation between Morrey spaces and multiplier spaces. By fractal skills, we construct a counterexample to show that the scope of the indexτofMr,pt,τ(ℝn)is sharp. As an application, we consider a Schrödinger type operator with potentials inMr,pt,τ(ℝn).

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

Elliptic equations with discontinuous coefficients in generalized Morrey spaces

2017 ◽  
Vol 3 (3) ◽  
pp. 728-762 ◽  
Author(s):  
Giuseppe Di Fazio ◽  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano
Keyword(s):  
Elliptic Equations ◽  
Discontinuous Coefficients ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces
Sign in / Sign up

Export Citation Format

Share Document