1,720,970 research outputs found
On the maximal directional hilbert transform in three dimensions
No full textWe establish the sharp growth rate, in terms of cardinality, of the Lp norms of the maximal Hilbert transform Hω along finite subsets of a finite order lacunary set of directions ω c R3, answering a question of Parcet and Rogers in dimension n = 3. Our result is the first sharp estimate for maximal directional singular integrals in dimensions greater than 2. The proof relies on a representation of the maximal directional Hilbert transform in terms of a model maximal operator associated to compositions of 2D angular multipliers, as well as on the usage of weighted norm inequalities, and their extrapolation, in the directional setting
A sharp estimate for the Hilbert transform along finite order lacunary sets of directions
Full text linkLet be a nonnegative integer and be a lacunary set of directions of order . We show that the norms, , of the maximal directional Hilbert transform in the plane are comparable to . For vector fields with range in a lacunary set of of order and generated using suitable combinations of truncations of Lipschitz functions, we prove that the truncated Hilbert transform along the vector field , is -bounded for all . These results extend previous bounds of the first author with Demeter, and of Guo and Thiele.20 pages, 2 figures. Submitted. Changes: clarified the definition of D-lacunary set and streamlined the notatio
Singular integrals along lacunary directions in Rn
No full textA recent result by Parcet and Rogers is that finite order lacunarity characterizes the boundedness of the maximal averaging operator associated to an infinite set of directions in Rn. Their proof is based on geometric-combinatorial coverings of fat hyperplanes by two-dimensional wedges. Seminal results by Nagel-Stein-Wainger relied on geometric coverings of n-dimensional nature. In this article we find the sharp cardinality estimate for singular integrals along finite subsets of finite order lacunary sets in all dimensions. Previous results only covered the special case of the directional Hilbert transform in dimensions two and three. The proof is new in all dimensions and relies, among other ideas, on a precise covering of the n-dimensional Nagel-Stein-Wainger cone by two-dimensional Parcet-Rogers wedges
Maximal subspace averages
Full text linkWe study maximal operators associated to singular averages along finite subsets of the Grassmannian of -dimensional subspaces of . The well studied case corresponds to the the directional maximal function with respect to arbitrary finite subsets of . We provide a systematic study of all cases and prove essentially sharp bounds for the maximal subspace averaging operator in terms of the cardinality of , with no assumption on the structure of . In the codimension case, that is , we prove the precise critical weak -bound.
Drawing on the analogy between maximal subspace averages and -Nikodym maximal averages, we also formulate the appropriate maximal Nikodym conjecture for general . In this context, we prove the best possible -bound for the -Nikodym maximal function for all combinations of dimension and codimension.
Our estimates rely on Fourier analytic almost orthogonality principles, combined with polynomial partitioning, but we also use spatial analysis based on the precise calculation of intersections of -dimensional plates in .40 pages, 1 figure, submitted for publicatio
Maximal directional operators along algebraic varieties
Full text linkWe establish the sharp growth order, up to epsilon losses, of the -norm of the maximal directional averaging operator along a finite subset of a polynomial variety of arbitrary dimension , in terms of cardinality. This is an extension of the works by Córdoba, for one-dimensional manifolds, Katz for the circle in two dimensions, and Demeter for the 2-sphere. For the case of directions on the two-dimensional sphere we improve by a factor of on the best known bound, due to Demeter, and we obtain a sharp estimate for our model operator. Our results imply new -estimates for Kakeya-type maximal functions with tubes pointing along polynomial directions. Our proof technique is novel and in particular incorporates an iterated scheme of polynomial partitioning on varieties adapted to directional operators, in the vein of Guth, Guth-Katz, and Zahl.34 pages, final version, incorporates the comments of the anonymous referees; to appear in Amer. J. Mat
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
A metric approach to sparse domination
No full textWe present a general approach to sparse domination based on single-scale Lp-improving as a key assumption. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ–Hytönen–Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón–Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of Rn
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe 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
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