Liguang Liu
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View article: Nontrivial nonnegative weak solutions to fractional $p$-Laplace inequalities
Nontrivial nonnegative weak solutions to fractional $p$-Laplace inequalities Open
For the nonlocal quasilinear fractional $p$-Laplace operator $(-Δ)^s_p$ with $s\in (0,1)$ and $p\in(1,\infty)$, we investigate the nonexistence and existence of nontrivial nonnegative solutions $u$ in the local fractional Sobolev space $W_…
View article: Geochemistry, Sr-Nd Isotope Compositions, and U-Pb Chronology of Apatite from Kimberlite in Wafangdian, North China Craton: Constraints on the Late Magmatic Processes
Geochemistry, Sr-Nd Isotope Compositions, and U-Pb Chronology of Apatite from Kimberlite in Wafangdian, North China Craton: Constraints on the Late Magmatic Processes Open
Diamondiferous kimberlites occur in the Wafangdian area in the eastern part of the North China Craton (NCC). In order to better constrain their magmatic source and emplacement time, we have investigated apatite from two kimberlites, i.e., …
View article: Integrating Capacity and Autonomy in Evaluating the Quality of Governance: A Case of China’s Capital Markets and Local Debt Crisis
Integrating Capacity and Autonomy in Evaluating the Quality of Governance: A Case of China’s Capital Markets and Local Debt Crisis Open
View article: Bricolage and Growth Hacking: Two Smart Concepts of Creating a Business Lacking Resources
Bricolage and Growth Hacking: Two Smart Concepts of Creating a Business Lacking Resources Open
The chapter presents two smart concepts of creating a new business without or with only low budget. Thus, it applies particularly e.g., for either students, refugees and/or people from developing countries. “Bricolage” stands for a behavio…
View article: Multiplication between Hardy spaces and their dual spaces
Multiplication between Hardy spaces and their dual spaces Open
View article: Intrinsic nature of the Stein-Weiss $H^1$-inequality
Intrinsic nature of the Stein-Weiss $H^1$-inequality Open
This paper explores the intrinsic nature of the celebrated Stein-Weiss $H^1$-inequality $$ \|I_s u\|_{L^\frac{n}{n-s}}\lesssim \|u\|_{L^1}+\|\vec{R}u\|_{L^{1}}=\|u\|_{H^1} $$ through the tracing and duality laws based on Riesz's singular i…
View article: New Calderón Reproducing Formulae with Exponential Decay on Spaces of Homogeneous Type
New Calderón Reproducing Formulae with Exponential Decay on Spaces of Homogeneous Type Open
Assume that $(X, d, μ)$ is a space of homogeneous type in the sense of Coifman and Weiss. In this article, motivated by the breakthrough work of P. Auscher and T. Hytönen on orthonormal bases of regular wavelets on spaces of homogeneous ty…
View article: New Calder\'on Reproducing Formulae with Exponential Decay on Spaces of Homogeneous Type
New Calder\'on Reproducing Formulae with Exponential Decay on Spaces of Homogeneous Type Open
Assume that $(X, d, \mu)$ is a space of homogeneous type in the sense of Coifman and Weiss. In this article, motivated by the breakthrough work of P. Auscher and T. Hyt\"onen on orthonormal bases of regular wavelets on spaces of homogeneou…
View article: Intrinsic Structures of Certain Musielak-Orlicz Hardy Spaces
Intrinsic Structures of Certain Musielak-Orlicz Hardy Spaces Open
For any $p\in(0,\,1]$, let $H^{Φ_p}(\mathbb{R}^n)$ be the Musielak-Orlicz Hardy space associated with the Musielak-Orlicz growth function $Φ_p$, defined by setting, for any $x\in\mathbb{R}^n$ and $t\in[0,\,\infty)$, $$ Φ_{p}(x,\,t):= \begi…
View article: Besov-type and Triebel–Lizorkin-type spaces associated with heat kernels
Besov-type and Triebel–Lizorkin-type spaces associated with heat kernels Open