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L\sp p estimates for uniformly hypoelliptic operators with discontinuous coefficients on homogeneous groups
No full text
Schauder estimates for parabolic nondivergence operators of Hörmander type
No full textLet be a system of real smooth vector fields
satisfying H\"{o}rmander's rank condition in a bounded domain of
. Let be a symmetric, uniformly positive definite matrix of real
functions defined in a domain . For operators
of kind
we prove local a-priori estimates of Schauder-type, in the natural (parabolic)
spaces defined by the vector fields
and the distance induced by them. Namely, for
and we prove%
\[
\left\Vert u\right\Vert _{C^{k+2,\alpha}\left( U^{\prime}\right) }\leqslant
c\left\{ \left\Vert Hu\right\Vert _{C^{k,\alpha}\left( U\right)
}+\left\Vert u\right\Vert _{L^{\infty}\left( U\right) }\right\} .
\
Estimates of BMO-type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs
No full textLet us consider the class of nonvariational uniformly
hypoelliptic operators:
where: is a system of H\"{o}rmander vector fields
in (), is a
uniformly elliptic matrix, and the functions are
continuous, with a suitable control on the modulus of continuity. We prove
that:
for domains that are regular in a suitable
sense. Moreover, the space in the above estimate can be replaced with a
scale of spaces of the kind studied by Spanne. To get this estimate, several
results are proved, regarding singular and fractional integrals on general
spaces of homogeneous type, in relation with function spaces of type
Non-divergence equations structured on Hörmander vector fields: heat kernels and Harnack inequalities.
No full textIn this work we deal with linear second order partial differential operators
of the following type:%
where is a system of real H\"{o}rmander's vector
fields in some bounded domain of , is a real symmetric
uniformly positive definite matrix in . The coefficients are H\"{o}lder continuous
on with respect to the parabolic
CC-metric (where is
the Carnot-Carath\'{e}odory distance induced by the vector fields 's).
We prove the existence of a fundamental solution
for , satisfying natural properties and sharp Gaussian bounds of the kind:%
\begin{gather*}
\frac{e^{-cd\left( x,y\right) ^{2}/\left( t-s\right) }}{c\left\vert
B\left( x,\sqrt{t-s}\right) \right\vert }\leq h\left( t,x;s,y\right) \leq
c\frac{e^{-d\left( x,y\right) ^{2}/c\left( t-s\right) }}{\left\vert
B\left( x,\sqrt{t-s}\right) \right\vert }\\
\left\vert X_{i}h\left( t,x;s,y\right) \right\vert \leq\frac{c}{\sqrt{t-s}%
}\frac{e^{-d\left( x,y\right) ^{2}/c\left( t-s\right) }}{\left\vert
B\left( x,\sqrt{t-s}\right) \right\vert }\\
\left\vert X_{i}X_{j}h\left( t,x;s,y\right) \right\vert +\left\vert
\partial_{t}h\left( t,x;s,y\right) \right\vert \leq\frac{c}{t-s}%
\frac{e^{-d\left( x,y\right) ^{2}/c\left( t-s\right) }}{\left\vert
B\left( x,\sqrt{t-s}\right) \right\vert }%
\end{gather*}
where denotes the Lebesgue
measure of the -ball . We then use these properties
of as a starting point to prove a \textit{scaling invariant }Harnack
inequality for positive solutions to , when . All the
constants in our estimates and inequalities will depend on the coefficients
only through their H\"{o}lder norms and the ellipticity
constant of the matrix
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On the lifting and approximation theorem for nonsmooth vector fields
No full textWe prove a version of Rothschild-Stein's theorem of lifting and approximation and some related results in the context of nonsmooth Hörmander's vector fields for which the highest order commutators are only Hölder continuous. The theory explicitly covers the case of one vector field having weight two while the others have weight one
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