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Register a new userCharacterization of inclusion relations between wiener amalgam and some classical spaces
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In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also obtain the optimal inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spaces $W_{p,q}^s$, which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [J. Funct. Anal. 268 (2015), 239-254]. In addition, we establish some mild characterizations of inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces, which relates some modern inequalities to classical inequalities.
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We study the boundedness on the Wiener amalgam spaces $W^{p,q}_s$ of Fourier multipliers with symbols of the type $e^{imu(xi)}$, for some real-valued functions $mu(xi)$ whose prototype is $|xi|^{beta}$ with $betain (0,2]$. Under some suitable assumptions on $mu$, we give the characterization of $W^{p,q}_srightarrow W^{p,q}$ boundedness of $e^{imu(D)}$, for arbitrary pairs of $0< p,qleq infty$. Our results are an essential improvement of the previous known results, for both sides of sufficiency and necessity, even for the special case $mu(xi)=|xi|^{beta}$ with $1<beta<2$.
In this paper, we introduce the notion of martingale Hardy-amalgam spaces: $ H^s_{p,q},,,mathcal{Q}_{p,q}$ and $mathcal{P}_{p,q}$. We present two atomic decompositions for these spaces. The dual space of $H^s_{p,q}$ for $0<ple qle 1$ is shown to be a Campanato-type space.
We present in this paper some embeddings of various dyadic martingale Hardy-amalgam spaces $H^S_{p,q},,, H^s_{p,q},,,H^*_{p,q},,,mathcal{Q}_{p,q}$ and $mathcal{P}_{p,q}$ of the real line. In the same settings, we characterize the dual of $H^s_{p,q}$ for large $p$ and $q$. We also introduce a Garsia-type space $mathcal{G}_{p,q}$ and characterize its dual space.
Let $Dinmathbb{N}$, $qin[2,infty)$ and $(mathbb{R}^D,|cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, via an auxiliary function space $mathrm{WE}^{1,,q}(mathbb R^D)$ defined via wavelet expansions, the authors establish the Riesz transform characterization of Triebel-Lizorkin spaces $dot{F}^0_{1,,q}(mathbb{R}^D)$. As a consequence, the authors obtain the Fefferman-Stein decomposition of Triebel-Lizorkin spaces $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Finally, the authors give an explicit example to show that $dot{F}^0_{1,,q}(mathbb{R}^D)$ is strictly contained in $mathrm{WE}^{1,,q}(mathbb{R}^D)$ and, by duality, $mathrm{WE}^{infty,,q}(mathbb{R}^D)$ is strictly contained in $dot{F}^0_{infty,,q}(mathbb{R}^D)$. Although all results when $D=1$ were obtained by C.-C. Lin et al. [Michigan Math. J. 62 (2013), 691-703], as was pointed out by C.-C. Lin et al., the approach used in the case $D=1$ can not be applied to the case $Dge2$, which needs some new skills.
We consider Littlewood-Paley functions associated with non-isotropic dilations. We prove that they can be used to characterize the parabolic Hardy spaces of Calder{o}n-Torchinsky.
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