Multilinear commutators of fractional integrals over Morrey spaces with non-doubling measures

Tao, Xiangxing; Zheng, Tao

doi:10.1007/s00030-010-0096-8

Cited by 12 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We do not go into the details. In fact, after writing the paper, the authors are made aware that Tao and Zheng [21] obtained some results in this direction.…”

Section: Remark 21mentioning

confidence: 99%

Multilinear fractional integrals on Morrey spaces

Iida

Sato

Sawano

et al. 2012

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

show abstract

“…We do not go into the details. In fact, after writing the paper, the authors are made aware that Tao and Zheng [21] obtained some results in this direction.…”

Section: Remark 21mentioning

confidence: 99%

Multilinear fractional integrals on Morrey spaces

Iida

Sato

Sawano

et al. 2012

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

show abstract

“…Although such a measure does not satisfy the doubling condition, many results on the classical Calderón-Zygmund theory have been proved to still hold; see, for example, [8,16,17] and some references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Maximal bilinear Calderón--Zygmund operators of type $\omega(t)$ on non-homogeneous space

Zheng¹,

Wang²,

Xiao³

2015

Ann. Funct. Anal.

Self Cite

View full text Add to dashboard Cite

Let (X , d, µ) be a geometrically doubling metric space and assume that the measure µ satisfies the upper doubling condition. In this paper, the authors, by invoking a Cotlar type inequality, show that the maximal bilinear Calderón-Zygmund operators of type ω(t) is bounded fromMoreover, if w = (w 1 , w 2 ) belongs to the weight class A ρ p (µ), using the John-strömberg maximal operator and the John-strömberg sharp maximal operator, the authors obtain a weighted weak type estimate L p1 (w 1 ) × L p2 (w 2 ) → L p,∞ (v w ) for the maximal bilinear Calderón-Zygmund operators of type ω(t). By weakening the assumption of ω ∈ Dini(1/2) into ω ∈ Dini(1), the results obtained in this paper are substantial improvements and extensions of some known results, even on Euclidean spaces R n .

show abstract

“…Moreover, the Morrey spaces boundedness of I α was discussed by some authors, see [39,62] and [63], for example. In 2012, Iida et al [40] gave a result, where the range of indexes is sharp.…”

Section: Bilinear Fractional Integral Operatorsmentioning

confidence: 98%

Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces

Ding

Mei

2014

Potential Anal

View full text Add to dashboard Cite

Denote by T and I α the bilinear Calderón-Zygmund operator and bilinear fractional integrals, respectively. In this paper we give the boundedness and compactness of the commutators [T , b] and compact operators (if b ∈ CMO, the BMO-closure of C ∞ c ) from L p 1 ,λ 1 × L p 2 ,λ 2 to L p,λ for some suitable indexes λ, λ 1 , λ 2 and p, p 1 , p 2 . As an application of our results, we give also the boundedness and compactness of the commutators formed by the bilinear pseudodifferential operators on Morrey spaces.

show abstract

Multilinear commutators of fractional integrals over Morrey spaces with non-doubling measures

Cited by 12 publications

References 7 publications

Multilinear fractional integrals on Morrey spaces

Multilinear fractional integrals on Morrey spaces

Maximal bilinear Calderón--Zygmund operators of type $\omega(t)$ on non-homogeneous space

Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces

Contact Info

Product

Resources

About