We prove sharp improved Sobolev inequalities on $\mathbb{S}^n$, $n\ge 4$, for functions whose critical density $|u|^{2n/(n-2)}$ has zero barycenter, without any symmetry assumption. The Dirichlet coefficient improves by the optimal factor $2^{-2/n}$, while the coefficient of the $L^2$ term remains one. Equality holds precisely for constant functions. This establishes the sharp form of Aubin's improved Sobolev inequality in every dimension $n\ge4$.
We prove sharp improved Sobolev inequalities on $\mathbb S^n$, $n\ge3$, for antipodally even functions and for axially symmetric functions whose critical density $|u|^{2n/(n-2)}$ has zero barycenter. In both cases, the Dirichlet coefficient improves by the optimal factor $2^{-2/n}$, while the coefficient of the $L^2$ t...
We prove the local $L^4$ Strichartz estimate without derivative loss for the Zakharov--Kuznetsov flow on $\mathbb{R}\times\mathbb{T}$. This reaches the sharp spatial regularity endpoint and implies the embedding $X^{0,b}\hookrightarrow L^4$ for every $b>1/2$. The proof reduces the estimate to a semi-algebraic mixed-mea...
E. Başakoğlu, Wen-Ting Hu, Yu-Zhao Wang et al.· 0 citations
In this paper, it is proved that the commutator $\mathcal{H}_{β,b}$ which is generated by the $n$-dimensional fractional Hardy operator $\mathcal{H}_β$ and $b\in \dot{Λ}_α(\mathbb{R}^n)$ is bounded from $L^P(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$, where $0
Qin Zheng, Zun-Wei Fu· Communications in Mathematic...· 1 citation
We prove the Trudinger inequality with exponent $\frac{s}{s-1}$ for $M^{1,s}$ Sobolev spaces on metric measure spaces under the sole measure growth assumption $\mu(B(x,r))\ge br^s$. This improves the previously known exponential integrability with power one. Our argument also yields sharp asymptotic bounds for the Sobo...
R. Alvarado, Ahmed Dughayshim, P. Hajłasz· 0 citations
We develop a semigroup interpolation method for sharp logarithmic Sobolev inequalities using spectral calculus and estimates of $\mathrm{Re}\langle\,Lx,x^2\rangle_2$, where $L$ generates an auxiliary symmetric quantum Markov semigroup. We apply the method to free groups and to crossed products of a finite von Neumann a...
We prove that the strong spherical maximal operator in $\mathbb{R}^n$ is bounded on $L^p$ for $n\geq4$ and $p>(n+1)/(n-1)$. This establishes the conjecture of Hickman and Zahl in the remaining dimensions. The main ingredient is a local $L^2$ estimate for the pieces obtained by a dyadic decomposition in the normal varia...
Ming-Feng Chen· 1 citation· ⚡1
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