Results 21 to 30 of about 516 (75)

FLOW WITH $A_{\infty }(\mathbb{R})$ DENSITY AND TRANSPORT EQUATION IN $\text{BMO}(\mathbb{R})$

Forum of Mathematics, Sigma, 2019
We show that, if $b\in L^{1}(0,T;L_{\operatorname{loc}}^{1}(\mathbb{R}))$ has a spatial derivative in the John–Nirenberg space $\operatorname{BMO}(\mathbb{R})$, then it generates a unique flow $\unicode[STIX]{x1D719}(t,\cdot )$ which has an $A_{\infty }(\
RENJIN JIANG, KANGWEI LI, JIE XIAO
doaj   +1 more source

Sublinear equations and Schur's test for integral operators

, 2017
We study weighted norm inequalities of $(p,r)$-type, $ \Vert \mathbf{G} (f \, d \sigma) \Vert_{L^r(\Omega, d\sigma)} \le C \Vert f \Vert_{L^p(\Omega, \sigma)}, \quad \forall \, f \in L^p(\sigma),$ for $0 1$, where $\mathbf{G}(f d \sigma)(x)=\int_\Omega G(
Verbitsky, Igor E.
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Endpoint bounds for quasiradial Fourier multipliers

, 2016
We consider quasiradial Fourier multipliers, i.e. multipliers of the form $m(a(\xi))$ for a class of distance functions $a$. We give a necessary and sufficient condition for the multiplier transformations to be bounded on $L^p$ for a certain range of $p$.
Kim, Jongchon
core   +1 more source

The John–Nirenberg Inequality of BLO With Hausdorff Content

Journal of Function Spaces
MSC2020 Classification: 42B35, 28A12 ...
Chenglong Fang
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Some sharp bilinear space-time estimates for the wave equation

, 2015
We prove a family of sharp bilinear space-time estimates for the half-wave propagator. As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.Comment: 18 ...
Bez, Neal, Jeavons, Chris, Ozawa, Tohru
core   +1 more source

A bundling problem revisited [PDF]

, 2016
It was conjectured by M. Glasser and S. Davison and later proved by A. Eremenko that the certain animals should gather close to each other in order to decrease the total heat loss.
Ivanisvili, Paata
core   +1 more source

Trudinger–Moser type inequalities with logarithmic weights in fractional dimensions

Advanced Nonlinear Studies
The purpose of this paper is two-fold. First, we derive sharp Trudinger–Moser inequalities with logarithmic weights in fractional dimensions:  sup∫01w(r)u′(r)β+2dλα1/(β+2)≤1∫01eμα,θ,γuβ+2β+11−γdλθ 1 and γ = 1 are also be considered in this part to ...
Xue Jianwei, Zhang Caifeng, Zhu Maochun
doaj   +1 more source

Hardy inequalities with Bessel pair for Dunkl operator

Advanced Nonlinear Studies
Using the notion of a Bessel pair, we study the Hardy type inequalities in the setting of Dunkl operator. We also establish a general symmetrization principle for weighted Hardy type inequalities with Dunkl operator in the situation that the standard ...
Nguyen Duy Tuan, Nguyen Phong Van, Pham Hien Thi Thu   +2 more
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Boundedness of Maximal Operators of Schr\"odinger Type with Complex Time

, 2012
Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \geq 0$ for which boundedness from the Sobolev space $H^s(\mathbb{R})$ into $L^2(\mathbb{R ...
Bailey, Andrew D.
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Accretivity and form boundedness of second order differential operators

, 2019
Let $\mathcal{L}$ be the general second order differential operator with complex-valued distributional coefficients $A=(a_{jk})_{j, k=1}^n$, $\vec{b}=(b_{j})_{j=1}^n$, and $c$ in an open set $\Omega \subseteq \mathbb{R}^n$ ($n \ge 1$), with principal ...
Maz'ya, V. G., Verbitsky, I. E.
core   +1 more source