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The fractional integral between Orlicz and BMO(phi) spaces on spaces of homogeneous type
(Faculty of Mathematics and Physics of Charles University, 2003-07)
In this work we give sufficient and necessary conditions for the boundednessof the fractional integral operator acting between weighted Orlicz spaces and suitableBMOφ spaces, in the general setting of spaces of homogeneous ...
On the geometry of spaces of homogeneous type and the democracy of Haar systems in Lorentz spaces
(Academic Press Inc Elsevier Science, 2019-08)
We explore the relation of the geometric structure of the underlying space and the democratic character of Haar systems in Lorentz spaces. We show that, aside from homogeneity, some particular behavior of the space at large ...
Function spaces of coercivity for the fractional Laplacian in spaces of homogeneous type
(Duke University Press, 2019-05)
We combine dyadic analysis through Haar type wavelets defined on Christ´s families of generalized cubes, and Lax-Milgram theorem, in order to prove existence of Green´s functions for fractional Laplacians on some function ...
Discrete approximation of spaces of homogeneous type
(Springer, 2009-01)
In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601-628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453-1459, 1998) to get ...
Homogeneous spaces, algebraic K-theory and cohomological dimension of fields
(European Mathematical Society, Suiza, 2022)
Let q be a non-negative integer. We prove that a perfect field K has cohomological dimension at most q + 1 if, and only if, for any finite extension L of K and for any homogeneous space Z under a smooth linear connected ...
Curves in homogeneous spaces and their contact with 1-dimensional orbits
(Springer, 2011-10-01)
Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose ...
Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type
(Elsevier, 2014-08)
We give sufficient conditions on a real number β and on a closed set F in a general space of homogeneous type (X,d,μ)(X,d,μ) in such a way that μ(B(x,d(x,F)))βμ(B(x,d(x,F)))β becomes a Muckenhoupt weight. In order to prove ...
On Newton-Sobolev spaces
(Kossuth Lajos Tudomanyegyetem, 2017-01)
Newton-Sobolev spaces, as presented by N. Shanmugalingam, describe a way to extend Sobolev spaces to the metric setting via upper gradients, for metric spaces with ´sucient´ paths of nite length. Sometimes, as is the case ...
Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces
(Polish Acad Sciences Inst MathematicsWarsawPolónia, 2004)
EQUIGEODESICS ON FLAG MANIFOLDS
(Univ HoustonHoustonEUA, 2011)