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Register a new userSharp estimates of unimodular Fourier multipliers on Wiener amalgam spaces
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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 $1<beta<2$.
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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.
By a new method derived from Nicola--Primo--Tabacco[24], we study the boundedness on $alpha$-modulation spaces of unimodular multipliers with symbol $e^{imu(xi)}$. Comparing with the previous results, the boundedness result is established for a larger family of unimodular multipliers under weaker assumptions.
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.
For $ 0< lambda < frac{1}2$, let $ B_{lambda }$ be the Bochner-Riesz multiplier of index $ lambda $ on the plane. Associated to this multiplier is the critical index $1 < p_lambda = frac{4} {3+2 lambda } < frac{4}3$. We prove a sparse bound for $ B_{lambda }$ with indices $ (p_lambda , q)$, where $ p_lambda < q < 4$. This is a further quantification of the endpoint weak $L^{p_lambda}$ boundedness of $ B_{lambda }$, due to Seeger. Indeed, the sparse bound immediately implies new endpoint weighted weak type estimates for weights in $ A_1 cap RH_{rho }$, where $ rho > frac4 {4 - 3 p_{lambda }}$.
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