Linear operators and their commutators generated by Calderón–Zygmund operators on generalized Morrey spaces associated with ball Banach function spaces

Wei, Mingquan

doi:10.1007/s11117-022-00949-3

Cited by 7 publications

(3 citation statements)

References 42 publications

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“…Remark 3.2. As a special case, Wei and Yan obtained Proposition 3.1 and Proposition 3.2 in [25], it is pointed out here we get Proposition 3.1 and Proposition 3.2 via a direct way rather than properties of ball Banach function spaces in [25].…”

Section: Properties Of Mixed-norm Herz-slice Spacesmentioning

confidence: 64%

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

Kui¹,

Wang²,

Ge³

et al. 2021

Preprint

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The Gammarus zhouqiongi sp. nov. are described and illustrated from Xinjiang Uygur Autonomous Region, China. The new species is characterized by pereopods III-IV with long straight setae on posterior margins and inner ramus of uropod III 0.7 times as long as outer ramus. Detailed morphological comparisons with related species are discussed. The mitochondrial cytochrome c oxidase 1 (COI) sequence differs from the other Gammarus species in Xinjiang by 16.6%-32.4% in K2P distance. The mitochondrial (COI, 16S) and nuclear markers (28S, EF1α) show that the new species is an independent branch in the phylogenetic tree. A key to identify Gammarus species in the Xinjiang are also provided.

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Section: Properties Of Mixed-norm Herz-slice Spacesmentioning

confidence: 64%

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

Kui¹,

Wang²,

Ge³

et al. 2021

Preprint

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“…(ii) and (iii) in Lemma 2.8 are from [34,Lemma 2.4]. The proof of (i) and (iv) in Lemma 2.8 is similar to that of [18,Lemma 5]; we omit the details.…”

Section: Preliminariesmentioning

confidence: 94%

“…Later, Zhang et al [39] and Wang et al [33] introduced the weak Hardy space W H X (R n ) associated with X and developed its complete real-variable theory. Very recently, Wei et al [34] considered Herz-type space associated with X. For more recent developments about ball quasi-Banach function spaces on, we refer the reader to [7,19,31,36].…”

Section: Introductionmentioning

confidence: 99%

Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Wang

Yang

2020

Results Math

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Let X be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of H X (R n ), the Hardy space associated with X, via the Littlewood-Paley g-functions and g * λ -functions. Moreover, the authors obtain the boundedness of Calderón-Zygmund operators on H X (R n ). For the local Hardytype space h X (R n ) associated with X, the authors also obtain the boundedness of S 0 1,0 (R n ) pseudo-differential operators on h X (R n ) via first establishing the atomic characterization of h X (R n ). Furthermore, the characterizations of h X (R n ) by means of local molecules and local Littlewood-Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz-Hardy space, the Lorentz-Hardy space, the Morrey-Hardy space, the variable Hardy space, the Orlicz-slice Hardy space and their local versions. Some special cases of these applications are even new and, particularly, in the case of the variable Hardy space, the g * λ -function characterization obtained in this article improves the known results via widening the range of λ.As natural generalizations and substitutes of L p (R n ) with p ∈ (0, 1], a real-variable theory of classical Hardy spaces H p (R n ) was originally initiated by Stein and Weiss [51] and then systematically developed by Fefferman and Stein [17]. These celebrated articles [51] and [17] inspire many new ideas for the real-variable theory of function spaces. For instance, the characterizations of classical Hardy spaces reveal the important connections among various notions in harmonic analysis, such as harmonic functions, various maximal functions and various square functions.On another hand, due to the need from applications for more inclusive classes of function spaces than L p (R n ), many other function spaces are introduced; for instance, weighted Lebesgue spaces, Lorentz spaces, variable Lebesgue spaces, Orlicz spaces and Morrey spaces. These spaces and the Hardy-type spaces based on them have been investigated extensively. Associated with these spaces, an important concept about function spaces is the (quasi-)Banach function space, which is defined as follows (see, for instance, [6, Chapter 1] for more details).(iv) 1 E ∈ Y for any measurable set E ⊂ R n with finite measure. Here and thereafter, 1 E denotes the characteristic function of E.Moreover, a Banach space Y, consisting of measurable functions on R n , is called a Banach function space if it satisfies the above terms (i) through (iv) and(v) for any measurable set E ⊂ R n with finite measure, there exists a positive constant C (E) , depending on E, such that, for any f ∈ Y,One can show that Lebesgue spaces, Lorentz spaces, variable Lebesgue spaces and Orlicz spaces are (quasi-)Banach function spaces. However, weighted Lebesgue spaces, Herz spaces, Morrey spaces and Musielak-Orlicz spaces are not necessarily quasi-Banach function spaces (see, for instan...

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Fractional integral operator and its commutator on generalized Morrey spaces associated with ball Banach function spaces

Wei

2023

Fract Calc Appl Anal

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Linear operators and their commutators generated by Calderón–Zygmund operators on generalized Morrey spaces associated with ball Banach function spaces

Cited by 7 publications

References 42 publications

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Fractional integral operator and its commutator on generalized Morrey spaces associated with ball Banach function spaces

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Linear operators and their commutators generated by Calderón–Zygmund operators on generalized Morrey spaces associated with ball Banach function spaces

Cited by 7 publications

References 42 publications

A new Gammarus&nbsp;species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

A new Gammarus&nbsp;species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Fractional integral operator and its commutator on generalized Morrey spaces associated with ball Banach function spaces

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Product

Resources

About

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)

A new Gammarus species from Xinjiang Uygur Autonomous Region (China) with a key to Xinjiang freshwater gammarids (Crustacea, Amphipoda, Gammaridae)