Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates

The Anh Bui; Jun Cao; Luong Dang Ky; Dachun Yang; Sibei Yang

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Displaying similar documents to “Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates”

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Analysis and Geometry in Metric Spaces

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In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot groups of arbitrarly large step. Moreover, we prove some nonexistence results for semilinear equations in the Engel group, which is the simplest Carnot group that is not of type ★.

On Asymmetric Distances

Andrea C.G. Mennucci (2013)

Analysis and Geometry in Metric Spaces

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In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize...

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Nanoscale Systems: Mathematical Modeling, Theory and Applications

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A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb...

Bayesian Analysis for Robust Synthesis of Nanostructures

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Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Nanomaterials, because of their unique properties such as extremely small size and increased ratio of surface area to volume, have a great potential in many industrial applications that involve electronics, sensors, solar cells, super-strong materials, coatings, drug delivery, and nanomedicine. They have the potential also to improve the environment by direct applications of these materials to detect, prevent and remove pollutants. While nanomaterials present seemingly limitless possibilities,...

Compactness of Special Functions of Bounded Higher Variation

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Analysis and Geometry in Metric Spaces

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Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] the description of singularities of codimension n, the distributional jacobian Ju need not...

Neighborhood base at the identity of free paratopological groups

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In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

A. Perälä, J. A. Virtanen, L. Wolf (2013)

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We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

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Hasan Alkanjo (2013)

Concrete Operators

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In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..

On the inverse of the adjacency matrix of a graph

Alexander Farrugia, John Baptist Gauci, Irene Sciriha (2013)

Special Matrices

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A real symmetric matrix G with zero diagonal encodes the adjacencies of the vertices of a graph G with weighted edges and no loops. A graph associated with a n × n non–singular matrix with zero entries on the diagonal such that all its (n − 1) × (n − 1) principal submatrices are singular is said to be a NSSD. We show that the class of NSSDs is closed under taking the inverse of G. We present results on the nullities of one– and two–vertex deleted subgraphs of a NSSD. It is shown that...

A Formula for Popp’s Volume in Sub-Riemannian Geometry

Davide Barilari, Luca Rizzi (2013)

Analysis and Geometry in Metric Spaces

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For an equiregular sub-Riemannian manifold M, Popp’s volume is a smooth volume which is canonically associated with the sub-Riemannian structure, and it is a natural generalization of the Riemannian one. In this paper we prove a general formula for Popp’s volume, written in terms of a frame adapted to the sub-Riemannian distribution. As a first application of this result, we prove an explicit formula for the canonical sub- Laplacian, namely the one associated with Popp’s volume. Finally,...

Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Jinn-Liang Liu (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock...