Generalized Sobolev–Morrey estimates for hypoelliptic operators on homogeneous groups

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
V. S. Guliyev
Keyword(s):  
Hypoelliptic Operators ◽  
Homogeneous Groups ◽  
Morrey Estimates

scholarly journals Global Hölder estimates for hypoelliptic operators with drift on homogeneous groups

2012 ◽  
Vol 13 (2) ◽  
pp. 337 ◽  
Author(s):  
Yuexia Hou ◽  
Xiaojing Feng ◽  
Xuewei Cui
Keyword(s):  
Hypoelliptic Operators ◽  
Homogeneous Groups ◽  
Hölder Estimates

scholarly journals Weighted Sobolev–Morrey Estimates for Nondivergence Degenerate Operators with Drift on Homogeneous Groups

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2061
Author(s):  
Yuexia Hou
Keyword(s):  
Vector Fields ◽  
Real Vector ◽  
Ellipticity Condition ◽  
Homogeneous Groups ◽  
Mean Oscillation ◽  
Weighted Morrey Spaces ◽  
Uniform Ellipticity ◽  
Morrey Estimates ◽  
Degenerate Operator ◽  
Degenerate Operators

Let X0,X1,…,Xq(q<N) be real vector fields, which are left invariant on homogeneous group G, provided that X0 is homogeneous of degree two and X1,…,Xq are homogeneous of degree one. We consider the following nondivergence degenerate operator with drift L=∑i,j=1qaij(x)XiXj+a0(x)X0, where the coefficients aij(x), a0(x) belonging to vanishing mean oscillation space are bounded measurable functions. Furthermore, aij(x) satisfies the uniform ellipticity condition on Rq and a0(x)≠0. We obtain the local weighted Sobolev–Morrey estimates by applying the boundedness of commutators and interpolation inequalities on weighted Morrey spaces.

Self-monitoring and leadership in culturally heterogeneous and homogeneous groups

2003 ◽  
Author(s):  
Magdalene Hsien Chen Pua ◽  
Lynn R. Offermann ◽  
Catina M. Smith ◽  
Mary Sass ◽  
Craig R. Seal ◽  
...  
Keyword(s):  
Self Monitoring ◽  
Homogeneous Groups

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

The early stages of spontaneous forest regeneration on poor soils and continental sand dunes in northern Belgium

1983 ◽  
Vol 49 ◽  
Author(s):  
M. Van Miegroet
Keyword(s):  
Scots Pine ◽  
Age Differences ◽  
Forest Regeneration ◽  
Sand Dunes ◽  
Mixed Forest ◽  
Pedunculate Oak ◽  
White Poplar ◽  
Technical Problems ◽  
Homogeneous Groups ◽  
Invading Species

Spontaneous  natural regeneration under variable conditions on sandy soils and continental  sand dunes were analysed in 5 locations in N.E. Belgium.     The number of seedlings varies between 14.000 and 522.000/ha. The most  prominent invading species are red oak, pedunculate oak and Scots pine.    Two principal types of regeneration are recognized : homogeneous groups of  oak or pine and mixtures, predominantly composed by the same species.  Pioneers such as birch, willow, white poplar and wild black cherry do not  play an important role.    Social differentiation sets in quite early and is mainly provoked by age  differences. Therefore early silvicultural intervention is advisable. The  growth relationships between the species indicate that Scots pine is not in  danger of spontaneous elemination by other species. Because of the density  and variability of spontaneous forest regeneration, the conversion of pure  pine stands into mixed forest, using group regeneration to this end, poses no  real technical problems.

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