Related papers: Orlicz mixed chord integrals
We prove a general theorem showing that local good-$\lambda$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.
Anisotropic generalized Orlicz spaces have been investigated in many recent papers, but the basic assumptions are not as well understood as in the isotropic case. We study the greatest convex minorant of anisotropic $\Phi$-functions and…
In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calder\'on--Zygmund singular integral operator,…
We prove in this article the generalizations on the exponential Orlicz spaces Markov's - Bernstein's inequalities for algebraic polynomials and rational functions.
In this paper, we introduce first the mixed affine quermassintegrals. The Aleksandrov-Fenchel inequality for the mixed affine quermassintegrals is established. As an application, the Minkowski, Brunn-Minkowski inequalities for the mixed…
In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.
Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions we obtain several numerical radius inequalities for a bounded linear operator as well…
The Orlicz $\left( \ell_{2},\ell_{1}\right) $-mixed inequality states that $$ \left( \sum_{j_{1}=1}^{n}\left( \sum_{j_{2}=1}^{n}\left\vert A(e_{j_{1} },e_{j_{2}})\right\vert \right) ^{2}\right) ^{\frac{1}{2}}\leq\sqrt {2}\left\Vert…
The variation of a class of Orlicz moments with respect to the Asplund sum within the class of log-concave functions is demonstrated. Such a variational formula naturally leads to a family of dual Orlicz curvature measures for log-concave…
The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modulus of continuity we provide upper error bounds of such…
In this paper we obtain some weighted generalizations of Ostrowski type inequalities on time scales involving combination of weighted {\Delta}-integral means, i.e., a weighted Ostrowski type inequality on time scales involving combination…
We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces. To do this we prove the weak-weak type modular inequality of the…
In this paper, we deal with the asymmetric Orlicz zonotopes by using the method of shadow system. We establish the volume product inequality and volume ratio inequality for asymmetric Orlicz zonotopes, along with their equality cases.
New results and improvements in the study of nonparametric exponential and mixture models are proposed. In particular, different equivalent characterizations of maximal exponential models, in terms of open exponential arcs and Orlicz…
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
The boundedness (continuity) of composition operators from some function space to another one is significant, though there are few results about this problem. Thus, in this study, we provide necessary and sufficient conditions on the…
In this paper, we investigate necessary and sufficient conditions on the boundedness of composition operators on the Orlicz-Morrey spaces. The results of boundedness include Lebesgue and generalized Morrey spaces as special cases. Further,…
In this article, we will define the Orlicz space and the Orlicz-Sobolev space, and develop their topological properties. We will also examine their applications to partial differential equations (PDEs), with an emphasis on the use of…
The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone…