Displaying similar documents to “Estimates for the commutator of bilinear Fourier multiplier”

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces M K ˙ q , p ( · ) α ( · ) , λ ( ℝ n ) of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents α and p are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...

Commutators of the fractional maximal function on variable exponent Lebesgue spaces

Pu Zhang, Jianglong Wu (2014)

Czechoslovak Mathematical Journal

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Let M β be the fractional maximal function. The commutator generated by M β and a suitable function b is defined by [ M β , b ] f = M β ( b f ) - b M β ( f ) . Denote by 𝒫 ( ℝ n ) the set of all measurable functions p ( · ) : ℝ n → [ 1 , ∞ ) such that 1 < p - : = ess inf x ∈ ℝ n p ( x ) and p + : = ess sup x ∈ ℝ n p ( x ) < ∞ , and by ℬ ( ℝ n ) the set of all p ( · ) ∈ 𝒫 ( ℝ n ) such that the Hardy-Littlewood maximal function M is bounded on L p ( · ) ( ℝ n ) . In this paper, the authors give some characterizations of b for which [ M β , b ] is bounded from L p ( · ) ( ℝ n ) into L q ( · ) ( ℝ n ) , when p ( · ) ∈ 𝒫 ( ℝ n ) , 0 < β < n / p + and 1 / q ( · ) = 1 / p ( · ) - β / n with q ( · ) ( n - β ) / n ∈ ℬ ( ℝ n ) .

Variable Lebesgue norm estimates for BMO functions

Mitsuo Izuki, Yoshihiro Sawano (2012)

Czechoslovak Mathematical Journal

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In this paper, we are going to characterize the space BMO ( ℝ n ) through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space BMO ( ℝ n ) by using various function spaces. For example, Ho obtained a characterization of BMO ( ℝ n ) with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue...

On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

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In the paper we find conditions on the pair ( ω 1 , ω 2 ) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space ℳ p , ω 1 to another ℳ p , ω 2 , 1 < p < ∞ , and from the space ℳ 1 , ω 1 to the weak space W ℳ 1 , ω 2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.