Generalized Sobolev–Morrey estimates for hypoelliptic operators on homogeneous groups

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.

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Self-monitoring and leadership in culturally heterogeneous and homogeneous groups

PsycEXTRA Dataset ◽

10.1037/e518712013-298 ◽

2003 ◽

Author(s):

Magdalene Hsien Chen Pua ◽

Lynn R. Offermann ◽

Catina M. Smith ◽

Mary Sass ◽

Craig R. Seal ◽

...

Keyword(s):

Self Monitoring ◽

Homogeneous Groups

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Discussion Patterns of Homogeneous Groups of Repressers and Sensitizers Following Success and Failure

PsycEXTRA Dataset ◽

10.1037/e594802009-001 ◽

1966 ◽

Author(s):

Richard N. Carrera ◽

Arthur M. Cohen

Keyword(s):

Homogeneous Groups

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

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2020.57.1.1449 ◽

2020 ◽

Vol 57 (1) ◽

pp. 68-90 ◽

Cited By ~ 1

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.

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

Silva Gandavensis ◽

10.21825/sg.v49i0.968 ◽

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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