Related papers: The Adams trace theorem for product Morrey spaces
By using parallel corona decomposition, the Kerman-Sawyer trace inequality is extended from Lebesgue spaces to product Morrey spaces.
The paper presents a new short proof of one of Adams's theorems and a $t$-trace-class theorem for parabolic Morrey spaces.
The main aim of this article is to study non-singular version of Moser-Trudinger and Adams-Moser-Trudinger inequalities and the singular version of Moser-Trudinger equality in the Cartesian product of Sobolev spaces. As an application of…
The absolute value of matrices is used in order to give inequalities for the trace of products. An application gives a very short proof of the tracial matrix Hoelder inequality
In this paper we strengthen to Morrey-Lorentz spaces the famous trace principle introduced by Adams. More precisely, we show that Riesz potential $I_{\alpha}$ is continuous \begin{equation} \Vert I_{\alpha}f\Vert_{\mathcal{M}_{q,…
We establish Adams type Stein-Weiss inequality on global Morrey spaces on general homogeneous groups. Special properties of homogeneous norms and some boundedness results on global Morrey spaces play key roles in our proofs. As consequence,…
In this paper, we establish the sharp critical and subcritical trace Trudinger-Moser and Adams inequalities on the half spaces and prove the existence of their extremals through the method based on the Fourier rearrangement, harmonic…
To any well-behaved homology theory we associate a derived $\infty$-category which encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on algebraicity of certain homotopy categories and establish…
Moss' theorem, which relates Massey products in the $E_r$-page of the classical Adams spectral sequence to Toda brackets of homotopy groups, is one of the main tools for calculating Adams differentials. Working in an arbitrary symmetric…
We present several results of embedding type for parabolic Morrey spaces with or without mixed norms. Some other interpolation results for parabolic Morrey spaces are also given.
We obtain a trace Hardy inequality for the Euclidean space with a bounded cut $\Sigma\subset\mathbb R^d$, $d \ge 2$. In this novel geometric setting, the Hardy-type inequality non-typically holds also for $d = 2$. The respective Hardy…
In this work we obtain a transference theorem for Lebesgue spaces with $A_{\infty }$ weights, namely, starting from some uniform-norm inequalities it is possible to obtain similar inequalities in Lebesgue spaces with $A_{\infty }$ weights.…
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to…
We use the Morrey norm estimate for the imaginary power of the Laplacian to prove an interpolation inequality for the fractional power of the Laplacian on Morrey spaces. We then prove a Hardy-type inequality and use it together with the…
Let $\Omega\subseteq \mathbb{R}^{4}$ be a bounded domain with smooth boundary $\partial\Omega$. In this paper, we establish the following sharp form of the trace Adams' inequality in $W^{2,2}(\Omega)$ with zero mean value and zero Neumann…
We present some new inequalities related to determinant and trace for positive semidefinite block matrices by using symmetric tensor product, which are extensions of Fiedler-Markham's inequality and Thompson's inequality.
In this paper we prove the existence of extremal functions for the Adams-Moser-Trudinger inequality on the Sobolev space $H^{m}(\Omega)$, where $\Omega$ is any bounded, smooth, open subset of $\mathbb{R}^{2m}$, $m\ge 1$. Moreover, we extend…
Inequalities for product operators on mixed norm Lebesgue spaces and permuted mixed norm Lebesgue spaces are established. They depend only on inequalities for the factors and on the Lebesgue indices involved. Inequalities for the bivariate…
We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},d\mu)} \leq c \|\mu\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\mathbb{R}^{n},d\mathscr{L}^{n})}$$ hold for vector fields…
Motivated by Ruf-Sani's recent work, we prove an Adams type inequality and a singular Adams type inequality in the whole four dimensional Euclidean space. As applications of those inequalities, a class of elliptic partial differential…