Searcharxiv⌕ Search

arXiv subjects

Jingshi Xu

Publications and source records attributed to Jingshi Xu.

13 recordsLinked to original sources
arXiv2026

Equivalent norms and $φ$-transform of matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces

We introduce matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces associated with an expansive matrix $A$. Inspired by the $\A_p$-dimensions of matrix weight of Bu et al. (2025), we study the properties of matrix weight associated with $A$. Using the nice properties of matrix weight, we obtain that these spaces are equivalent with their corresponding averaging spaces and establish the discrete $φ$-transform of these spaces. Finally, we introduce matrix-weighted anisotropic Triebel-Lizorkin spaces for the limiting case $p=\infty$ and obtain their $φ$-transform. The relation between matrix-weighted anisotropic Triebel-Lizorkin spaces and matrix-weighted anisotropic Besov-type and Triebel-Lizorkin-type spaces is also studied.

math.FA↗
arXiv2026

Mixed Bourgain-Morrey spaces and their applications to boundedness of operators

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved. In addition, we give a description of the dual of mixed Bourgain-Morrey spaces and conclude the reflexivity of these spaces.

math.FA↗
arXiv2026

Precompactness in matrix weighted Bourgain-Morrey spaces

In this paper, we introduce matrix weighted Bourgain-Morrey spaces and obtain two sufficient conditions for precompact sets in matrix weighted Bourgain-Morrey spaces. We prove that the dyadic average operator is bounded on some matrix weighted Bourgain-Morrey spaces. With this result, we obtain the necessity for precompact sets in some matrix weighted Bourgain-Morrey spaces. The results are new even for the unweighted Bourgain-Morrey spaces.

math.FA↗
arXiv2025

On matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces

We introduce the homogeneous (inhomogeneous) matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces and obtain their equivalent norms. We also obtain their characterizations by Peetre type maximal functions, Lusin-area function, Littlewood-Paley $g_λ^{*}$-function, approximation, wavelet and atom. As an application, we obtain boundedness of pseudo-differential operators with symbols in the Hörmander classes and Hölder-Zygmund classes on inhomogeneous matrix weighted Bourgain-Morrey Triebel-Lizorkin spaces.

math.FA↗
arXiv2025

On the mixed Bourgain-Morrey spaces

We introduce the mixed Bourgain-Morrey spaces and obtain their preduals. The boundedness of Hardy-Littlewood maximal operator, iterated maximal operator, fractional integral operator, singular integral operator on these spaces is proved. The Littlewood-Paley theory for mixed Bourgain-Morrey spaces and their preduals are established. As applications, we consider wavelet characterizations for mixed Bourgain-Morrey spaces and a fractional chain rule in mixed Bourgain-Morrey Triebel-Lizorkin spaces. In addition, we give a description of the dual of mixed Bourgain-Morrey spaces and conclude the reflexivity of these spaces.

math.FA↗
arXiv2025

The preduals of Banach space valued Bourgain-Morrey spaces

Let $X$ be a Banach space such that there exists a Banach space $^\ast X$ and $ ( ^\ast X )^ \ast = X $. In this paper, we introduce $X$-valued Bourgain-Morrey spaces. We show that $^\ast X$-valued block spaces are the predual of $X$-valued Bourgain-Morrey spaces. We obtain the completeness, denseness and Fatou property of $^\ast X$-valued block spaces. We give a description of the dual of $X$-valued Bourgain-Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy-Littlewood maximal operator in vector valued block spaces is obtained.

math.FA↗
arXiv2025

Bourgain-Morrey-Lorentz spaces and operators on them

We introduce Bourgain-Morrey-Lorentz spaces and give a description of the predual of Bourgain-Morrey-Lorentz spaces via the block spaces. As an application of duality, we obtain the boundedness of Hardy-Littlewood maximal operator, sharp maximal operator, Calderón-Zygmund operator, fractional integral operator, commutator on Bourgain-Morrey-Lorentz spaces. Moreover, we obtain a weak Hardy factorization terms of Calderón-Zygmund operator in Bourgain-Morrey-Lorentz spaces. Using this result, we obtain a characterization of functions in $\BMO$ (the functions of ``bounded mean oscillation'') via the boundedness of commutators generated by them and a homogeneous Calderón-Zygmund operator. In the last, we show that the commutator generated by a function $b$ and a homogeneous Calderón-Zygmund operator is a compact operator on Bourgain-Morrey-Lorentz spaces if and only if $b$ is the limit of compactly supported smooth functions in $\BMO$.

math.FA↗
arXiv2025

Weighted Bourgain-Morrey-Besov type and Triebel-Lizorkin type spaces associated with operators

Let $(X,μ)$ be a space of homogeneous type satisfying $μ(X) =\infty$, the doubling property and the reverse doubling condition. Let $L$ be a nonnegative self-adjoint operator on $L^2(X)$ whose heat kernel enjoys a Gaussian upper bound. We introduce the weighted homogeneous Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces associated with the operator $L$. We obtain their continuous characterizations in terms of Peetre maximal functions, noncompactly supported functional calculus, heat kernel. Atomic and molecular decompositions of weighted homogeneous Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces are also given. As an application, we obtain the boundedness of the fractional power of $L$, the spectral multiplier of $L$ on Bourgain-Morrey-Besov type spaces and Triebel-Lizorkin type spaces.

math.FA↗
arXiv2025

The Weighted Grand Herz-Morrey-Lizorkin-Triebel Spaces with Variable Exponents

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we introduce weighted grand Herz-Morrey-Triebel-Lizorkin spaces with variable exponents and provide their equivalent quasi-norms via maximal functions.

math.FA↗
arXiv2025

Precompactness in bivariate metric semigroup-valued bounded variation spaces

In this paper, we show that if a set in bivariate metric semigroups-valued bounded variation spaces is pointwise totally bounded and joint equivariated then it is precompact. These spaces include bounded Jordan variation spaces, bounded Wiener variation spaces, bounded Waterman variation spaces, bounded Riesz variation spaces and bounded Korenblum variation spaces. To do so, we introduce the concept of equimetric set.

math.FA↗
arXiv2024

Precompact Sets in Matrix Weighted Lebesgue Spaces with Variable Exponent

In this paper, we first give a sufficiently condition for precompactness in the matrix-weighted Lebesgue spaces with variable exponent by translation operator. Then we obtain a criterion for precompactness in the matrix-weighted Lebesgue space with variable exponent by average operator. Next, we give a criterion for precompactness in the matrix-weighted Lebesgue space with variable exponent by approximate identity. Finally, precompactness in the matrix-weighted Sobolev space with variable exponent is also considered.

math.FA↗