Inspired by the sharp coefficient estimates established by Cho \emph{et al.}\cite{CKKLS2018} for starlike functions of order $\alpha$ in the unit disk, we investigate the corresponding problems for starlike mappings of order $\alpha$ defined on the unit ball of a complex Banach space. Employing Fr\'echet derivatives together with suitable auxiliary lemmas, we establish sharp upper bounds for the second-order Hankel determinant, the Fekete--Szeg\"o functional, and the Zalcman functional associated with this class of mappings. In each case, the obtained estimates are shown to be sharp by identifying the corresponding extremal mappings. Furthermore, our results reduce to the known one-dimensional sharp estimates when the underlying Banach space is the complex plane, thereby extending several classical results of Cho \emph{et al.} \cite{CKKLS2018} to the setting of complex Banach spaces.
In this paper, we establish several higher-dimensional generalizations of refined Bohr-type inequalities for bounded holomorphic functions mapping into the unit polydisk $\mathbb{P}\Delta(0;1_n)$ in $\mathbb{C}^n$. First, we formulate multidimensional analogues of sharp Bohr-type inequalities originally established by...
Though the sharp $L^{2}$-Caffarelli--Kohn--Nirenberg (CKN) inequalities have been extensively studied in the entire Euclidean spaces, the corresponding problem on domains whose boundary contains the origin remains largely unexplored. We investigate the sharp $L^{2}$-CKN inequalities on half-spaces and orthants $\mathbb...
L. Nguyen, Yukta Lodha, Guo-Zhen Lu et al.· 4 citations
We establish the bound for the second-order Hankel determinant $H_{2,2}(F) = A_2 A_4 - A_3^2$ associated with the class $\mathcal{C}_{B}^{\beta}(\mathbb{B})$ of normalized $\beta$-spirallike quasi-convex mappings of type $B$ on the open unit ball $\mathbb{B}$ of a complex Banach space. By utilizing a generalized framew...
M. B. Ahamed, Nabadwip Sarkar, Pradip Das· 0 citations
In this paper, we prove a sharp Fefferman--Stein-type estimate for the fractional Schr\"odinger equation, which can be regarded as a generalized Strichartz estimate for data in the Fourier Lebesgue space $\widehat{L^p}$. Then, as an application of the Fefferman--Stein inequality and its off-diagonal generalization, we...
In this paper we prove H\"older inequalities for the Besov-Morrey spaces $ \mathcal{N}^{s}_{u,p,q}(\mathbb{R}^{d}) $ and the Triebel-Lizorkin-Morrey spaces $ \mathcal{E}^{s}_{u,p,q}(\mathbb{R}^{d}) $. We observe that these Morrey smoothness spaces are pointwise multiplier spaces if certain conditions concerning the par...
The aim of this paper is twofold. First, we establish a Riesz conjugate theorem for weighted harmonic Bergman spaces. More precisely, we prove that if $f=u+iv$ is a harmonic $K$-quasiregular mapping in $\mathbb{D}$ and the real part $u$ belongs to the weighted harmonic Bergman space $a_\alpha^p$, $0<p<\infty$, then the...
H. Halder, Rohit Kumar· 1 citation· ⚡1
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