Related papers: Problems on spherical maximal functions
In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two…
In this note we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also study the size of the set of Lebesgue points with respect to convergence associated with such…
In this paper we study the solutions of different forms of fractional equations on the unit sphere $\mathbb{S}_{1}^{2}$ $\subset \mathbb{R}^{3}$ possessing the structure of time-dependent random fields. We study the correlation functions of…
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
In this paper, we delve into the fascinating realm of fractal calculus applied to fractal sets and fractal curves. Our study includes an exploration of the method analogues of the separable method and the integrating factor technique for…
We obtain $L^p-$estimates for the full and lacunary maximal functions associated to the twisted bilinear spherical averages given by \[\mathfrak{A}_t(f_1,f_2)(x,y)=\int_{\mathbb S^{2d-1}}f_1(x+tz_1,y)f_2(x,y+tz_2)\;d\sigma(z_1,z_2),\;t>0,\]…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…
Under certain general conditions, an explicit formula to compute the greatest delta-epsilon function of a continuous function is given. From this formula, a new way to analyze the uniform continuity of a continuous function is given.…
In this article a definition of optimal cover for fractal structures is proposed. Expression for Minkowsky dimension is rewritten in terms of functional equation on areas of covers that constructed for different scales.Given the definition,…
Some fixed point results are given for a class of functional contractions acting on (reflexive) triangular symmetric spaces. Technical connections with the corresponding theories over (standard) metric and partial metric spaces are also…
Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced…
In this paper we study the derived sets for the rational deformations of multiple zeta-star values. By using the theory of bounded variation functions, we will give function decompositions which describe the metric structure of the derived…
We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
For spherical and parabolic averages of the Fourier transform of fractal measures, we obtain new upper bounds on rates of decay by an "intermediate dimension" trick.
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we…
We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.
Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in…