Related papers: Multifractal analysis of the Brjuno function
We define the concept of regularity for bigraded modules and bigraded polynomial ring. In this setting we prove analogs of some of the classical results on $m$-regularity for graded modules over polynomial algebras.
The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joint spectra have been stated, the condition for holomorphy of…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed…
We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the…
Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition…
In this note, we give a simple proof of the pointwise BMO estimate for Poisson's equation. Then the Calder\'{o}n-Zygmund estimate follows by the interpolation and duality.
Inhomogeneous multinomial measures on the mixed symbolic spaces and the real line are given. By counting the zeros of the corresponding generalized Dirichlet polynomials, one obtains a probability measure whose Olsen's functions $b$ and $B$…
A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…
We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its…
We show that the product BMO space can be characterized by iterated commutators of a large class of Calder\'on-Zygmund operators. This result follows from a new proof of boundedness of iterated commutators in terms of the BMO norm of their…
We introduce multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic…
We describe the average behaviour of the Brjuno function in the neighbourhood of any given point of the unit interval. In particular, we show that its Lebesgue set is the set of Brjuno numbers and we fi nd the asymptotic behaviour of the…
In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the…
In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function…
In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…
We obtain an explicit determinantal formula for the multiplicity of any point on a classical Schubert variety.
We prove that certain roots of the Bernstein-Sato polynomial (i.e. b-function) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain…