scholarly journals Compact embeddings of radial and subradial subspaces of some Besov-type spaces related to Morrey spaces

2013 ◽  
Vol 174 ◽  
pp. 121-139 ◽  
Author(s):  
Wen Yuan ◽  
Winfried Sickel ◽  
Dachun Yang
Keyword(s):  
Morrey Spaces ◽  
Compact Embeddings ◽  
Type Spaces ◽  
Besov Type Spaces

COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350021 ◽  
Author(s):  
DACHUN YANG ◽  
WEN YUAN ◽  
CIQIANG ZHUO
Keyword(s):  
Morrey Spaces ◽  
Schwartz Space ◽  
Complex Interpolation ◽  
Schwartz Functions ◽  
Type Spaces ◽  
Besov Type Spaces

Let θ ∈ (0, 1), s0, s1 ∈ ℝ, τ0, τ1 ∈ [0, ∞), p0, p1 ∈ (0, ∞), q0, q1 ∈ (0, ∞], s = s0(1 - θ) + s1θ, τ = τ0(1-θ) + τ1θ, [Formula: see text] and [Formula: see text]. In this paper, under the restriction [Formula: see text], the authors establish the complex interpolation, on Triebel–Lizorkin-type spaces, that [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz functions in [Formula: see text]. Similar results on Besov-type spaces and Besov–Morrey spaces are also presented. As a corollary, the authors obtain the complex interpolation for Morrey spaces that, for all 1 < p0 ≤ u0 < ∞, 1 < p1 ≤ u1 < ∞ and 1 < p ≤ u < ∞ such that [Formula: see text], [Formula: see text] and p0u1 = p1u0, [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz space in [Formula: see text]. It is known that, if p0u1 ≠ p1u0, these conclusions on Morrey spaces may not be true.

scholarly journals Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

2016 ◽  
Vol 146 (5) ◽  
pp. 905-927 ◽  
Author(s):  
António Caetano ◽  
Amiran Gogatishvili ◽  
Bohumír Opic
Keyword(s):  
Besov Spaces ◽  
Function Spaces ◽  
Lebesgue Spaces ◽  
Banach Function Spaces ◽  
Compact Embeddings ◽  
Type Spaces ◽  
Besov Type Spaces

There are two main aims of the paper. The first is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second is to extend the criterion for the precompactness of sets in the Lebesgue spaces Lp(ℝn), 1 ⩽ p < ∞, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces , into Lorentz-type spaces.

Characterizations of Besov-Type and Triebel–Lizorkin–Type Spaces via Averages on Balls

2017 ◽  
Vol 60 (3) ◽  
pp. 655-672 ◽  
Author(s):  
Ciqiang Zhuo ◽  
Winfried Sickel ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Sobolev Spaces ◽  
Morrey Spaces ◽  
Independent Interest ◽  
Special Cases ◽  
Type Spaces ◽  
Besov Type Spaces

AbstractLet ℓ ∊ ℕ and α > (§, 2ℓ). In this article, the authors establish equivalent characterizations of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaces via the sequence {ƒ-Bl,2-kƒ}k consisting of the diòerence between f and the ball average Bl,2-kƒ. These results lead to the introduction of Besov-type spaces, Triebel–Lizorkin-type spaces, and Besov–Morrey spaceswith any positive smoothness order onmetricmeasure spaces. As special cases, the authors obtain a new characterization ofMorrey–Sobolev spaces and Qα spaces with ∈ > (0, 1), which are of independent interest.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

scholarly journals The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takeshi Iida
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Type Spaces ◽  
Multilinear Maximal Function ◽  
Multilinear Maximal Operator ◽  
Littlewood Maximal Operator

The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function.

scholarly journals Non-smooth atomic decomposition of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces

2021 ◽  
Vol 15 (3) ◽  
Author(s):  
Helena F. Gonçalves
Keyword(s):  
Atomic Decomposition ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Variable Exponents ◽  
Atomic Decompositions ◽  
Local Means ◽  
Essential Tool ◽  
Pointwise Multipliers ◽  
Type Spaces

AbstractIn this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w , ϕ ( R n ) and $$F^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w , ϕ ( R n ) . Of big importance in general, and an essential tool here, are the characterizations of the spaces via maximal functions and local means, that we also present. These spaces were recently introduced by Wu et al. and cover not only variable 2-microlocal Besov and Triebel–Lizorkin spaces $$B^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) , q ( · ) w ( R n ) and $$F^{\varvec{w}}_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ F p ( · ) , q ( · ) w ( R n ) , but also the more classical smoothness Morrey spaces $$B^{s, \tau }_{p,q}({\mathbb {R}}^n)$$ B p , q s , τ ( R n ) and $$F^{s,\tau }_{p,q}({\mathbb {R}}^n)$$ F p , q s , τ ( R n ) . Afterwards, we state a pointwise multipliers assertion for this scale.

Corrigendum on ``Interpolating sequences on analytic Besov type spaces\"

2010 ◽  
Vol 59 (6) ◽  
pp. 1931-1934 ◽  
Author(s):  
Jordi Pau ◽  
Nicola Arcozzi ◽  
Daniel Blasi
Keyword(s):  
Interpolating Sequences ◽  
Type Spaces ◽  
Besov Type Spaces

scholarly journals Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Shengrong Wang ◽  
Jingshi Xu
Keyword(s):  
Morrey Spaces ◽  
Hardy Operator ◽  
Variable Exponents ◽  
Herz Spaces ◽  
Bmo Functions ◽  
Type Spaces

In this paper, we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of Herz spaces and Herz-Morrey spaces with variable exponents.

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