Hyponormality on an annulus with a general radial weight

2020 ◽  
Author(s):  
Houcine Sadraoui ◽  
Borhen Halouani
Keyword(s):  
Radial Weight

scholarly journals Bergman projection induced by radial weight

2021 ◽  
Vol 391 ◽  
pp. 107950
Author(s):  
José Ángel Peláez ◽  
Jouni Rättyä
Keyword(s):  
Bergman Projection ◽  
Radial Weight

On trace spaces of function spaces with a radial weight: the atomic approach

2010 ◽  
Vol 55 (8-10) ◽  
pp. 875-896 ◽  
Author(s):  
Dorothee D. Haroske ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Function Spaces ◽  
Radial Weight ◽  
Trace Spaces

scholarly journals Hopf-type theorem for self-shrinkers

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hilário Alencar ◽  
Gregório Silva Neto ◽  
Detang Zhou
Keyword(s):  
Fundamental Form ◽  
Mean Curvature ◽  
Type Theorem ◽  
Complex Function ◽  
Curvature Vector ◽  
Second Fundamental Form ◽  
Dimensional Euclidean Space ◽  
Position Vector ◽  
Weighted Mean Curvature ◽  
Radial Weight

Abstract In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three-dimensional Euclidean space ℝ 3 {{\mathbb{R}}^{3}} is a round sphere, provided its mean curvature and the norm of the its position vector have an upper bound in terms of the norm of its traceless second fundamental form. The example constructed by Drugan justifies that the hypothesis on the second fundamental form is necessary. We can also prove the same kind of rigidity results for surfaces with parallel weighted mean curvature vector in ℝ n {{\mathbb{R}}^{n}} with radial weight. These results are applications of a new generalization of Cauchy’s Theorem in complex analysis which concludes that a complex function is identically zero or its zeroes are isolated if it satisfies some weak holomorphy.

One weight inequality for Bergman projection and Calderón operator induced by radial weight

2021 ◽  
Author(s):  
Francisco Martín-Reyes ◽  
Pedro Ortega ◽  
José Peláez ◽  
Jouni Rättyä
Keyword(s):  
Bergman Projection ◽  
Radial Weight ◽  
Weight Inequality

scholarly journals Hankel operators induced by radial Bekollé–Bonami weights on Bergman spaces

2019 ◽  
Vol 296 (1-2) ◽  
pp. 211-238 ◽  
Author(s):  
José Ángel Peláez ◽  
Antti Perälä ◽  
Jouni Rättyä
Keyword(s):  
Bergman Space ◽  
Bergman Spaces ◽  
Hankel Operators ◽  
Weighted Bergman Space ◽  
Doubling Condition ◽  
Weighted Mean ◽  
Mean Oscillation ◽  
Radial Weight ◽  
Classical Setting

Abstract We study big Hankel operators $$H_f^\nu :A^p_\omega \rightarrow L^q_\nu $$ H f ν : A ω p → L ν q generated by radial Bekollé–Bonami weights $$\nu $$ ν , when $$1<p\le q<\infty $$ 1 < p ≤ q < ∞ . Here the radial weight $$\omega $$ ω is assumed to satisfy a two-sided doubling condition, and $$A^p_\omega $$ A ω p denotes the corresponding weighted Bergman space. A characterization for simultaneous boundedness of $$H_f^\nu $$ H f ν and $$H_{{\overline{f}}}^\nu $$ H f ¯ ν is provided in terms of a general weighted mean oscillation. Compared to the case of standard weights that was recently obtained by Pau et al. (Indiana Univ Math J 65(5):1639–1673, 2016), the respective spaces depend on the weights $$\omega $$ ω and $$\nu $$ ν in an essentially stronger sense. This makes our analysis deviate from the blueprint of this more classical setting. As a consequence of our main result, we also study the case of anti-analytic symbols.

scholarly journals DIRECTIONAL MAXIMAL OPERATORS AND RADIAL WEIGHTS ON THE PLANE

2013 ◽  
Vol 89 (3) ◽  
pp. 397-414
Author(s):  
HIROKI SAITO ◽  
HITOSHI TANAKA
Keyword(s):  
Maximal Operator ◽  
Unit Vector ◽  
Norm Inequality ◽  
Maximal Operators ◽  
Weighted Norm Inequality ◽  
Weighted Norm ◽  
Radial Weight ◽  
Orthogonality Principle ◽  
Image Position ◽  
Unit Vectors

AbstractLet $\Omega $ be the set of unit vectors and $w$ be a radial weight on the plane. We consider the weighted directional maximal operator defined by $$\begin{eqnarray*}{M}_{\Omega , w} f(x): = \sup _{x\in R\in \mathcal{B} _{\Omega }}\frac{1}{w(R)} \int \nolimits \nolimits_{R} \vert f(y)\vert w(y)\hspace{0.167em} dy,\end{eqnarray*}$$ where ${ \mathcal{B} }_{\Omega } $ denotes the set of all rectangles on the plane whose longest side is parallel to some unit vector in $\Omega $ and $w(R)$ denotes $\int \nolimits \nolimits_{R} w$. In this paper we prove an almost-orthogonality principle for this maximal operator under certain conditions on the weight. The condition allows us to get the weighted norm inequality $$\begin{eqnarray*}\Vert {M}_{\Omega , w} f\mathop{\Vert }\nolimits_{{L}^{2} (w)} \leq C\log N\Vert f\mathop{\Vert }\nolimits_{{L}^{2} (w)} ,\end{eqnarray*}$$ when $w(x)= \vert x\hspace{-1.2pt}\mathop{\vert }\nolimits ^{a} $, $a\gt 0$, and when $\Omega $ is the set of unit vectors on the plane with cardinality $N$ sufficiently large.

scholarly journals On the trace space of a Sobolev space with a radial weight

2008 ◽  
Vol 6 (3) ◽  
pp. 259-276 ◽  
Author(s):  
Helmut Abels ◽  
Miroslav Krbec ◽  
Katrin Schumacher
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Large Range ◽  
Weighted Sobolev Spaces ◽  
Full Description ◽  
Trace Space ◽  
Radial Weight ◽  
Trace Spaces

Our concern in this paper lies with trace spaces for weighted Sobolev spaces, when the weight is a power of the distance to a point at the boundary. For a large range of powers we give a full description of the trace space.

scholarly journals Rapid Parametric Human Modeling in 3D Garment Simulation

2019 ◽  
Vol 19 (1) ◽  
pp. 60-67 ◽  
Author(s):  
Jiajia Peng ◽  
Gaoming Jiang ◽  
Honglian Cong
Keyword(s):  
Straight Line Segment ◽  
Second Phase ◽  
Axial Deformation ◽  
Deformation Method ◽  
Straight Line ◽  
Radial Weight ◽  
Human Modeling ◽  
Different Types ◽  
Feature Information ◽  
Two Phases

Abstract To realize 3D garment simulation online and show the wearing effect of different body types, a method for rapid parametric human modeling is proposed in this article. The parameterization consists of two phases. In the first phase, the characteristic parameters of the sample model are extracted according to the different types of feature information. In the second phase, the deformation is realized by combining the axial deformation method and the radial weight. Thus, according to contrasts between the input measurement and the sample sizes, parametric human modeling is realized by deformation of the sample model. In the deformation stage, the axis curve is simplified to the straight-line segment in the axis deformation method, reducing the calculation. Comparative analysis and the results of experiments demonstrate that the better performance can be achieved at a higher speed, and this method realizes real-time parametric human modeling.

scholarly journals GAMA+KiDS: Alignment of galaxies in galaxy groups and its dependence on galaxy scale

2019 ◽  
Vol 628 ◽  
pp. A31 ◽  
Author(s):  
Christos Georgiou ◽  
Nora Elisa Chisari ◽  
Maria Cristina Fortuna ◽  
Henk Hoekstra ◽  
Konrad Kuijken ◽  
...  
Keyword(s):  
Galaxy Formation ◽  
Outer Region ◽  
Absolute Magnitude ◽  
Weight Functions ◽  
Shape Measurement ◽  
Galaxy Groups ◽  
Galaxy Formation And Evolution ◽  
Radial Weight ◽  
Significant Difference ◽  
Mass Assembly

Intrinsic galaxy alignments are a source of bias for weak lensing measurements as well as a tool for understanding galaxy formation and evolution. In this work, we measure the alignment of shapes of satellite galaxies, in galaxy groups, with respect to the brightest group galaxy (BGG), as well as alignments of the BGG shape with the satellite positions, using the highly complete Galaxy And Mass Assembly (GAMA) spectroscopic survey and deep imaging from the Kilo Degree Survey. We control systematic errors with dedicated image simulations and measure accurate shapes using the DEIMOS shape measurement method. We find a significant satellite radial alignment signal, which vanishes at large separations from the BGG. We do not identify any strong trends of the signal with galaxy absolute magnitude or group mass. The alignment signal is dominated by red satellites. We also find that the outer regions of galaxies are aligned more strongly than their inner regions, by varying the radial weight employed during the shape measurement process. This behaviour is evident for both red and blue satellites. BGGs are also found to be aligned with satellite positions, with this alignment being stronger when considering the innermost satellites, using red BGGs and the shape of the outer region of the BGG. Lastly, we measure the global intrinsic alignment signal in the GAMA sample for two different radial weight functions and find no significant difference.

scholarly journals Hilbert-type operator induced by radial weight

2021 ◽  
Vol 495 (1) ◽  
pp. 124689
Author(s):  
José Ángel Peláez ◽  
Elena de la Rosa
Keyword(s):  
Type Operator ◽  
Radial Weight ◽  
Hilbert Type
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