Publications (95)34.2 Total impact

Dataset: A preliminary version of the book

Dataset: Recenzie

Dataset: Matrix spaces

Dataset: Matrix spaces


Dataset: 8933


Article: On Hardy qinequalities
[Show abstract] [Hide abstract]
ABSTRACT: Some qanalysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha1} \int_0^x t^{\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the RiemannLiouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.Czechoslovak Mathematical Journal 03/2014; 64(3). · 0.29 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper some new Hardytype inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardytype inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed.Annals of Functional Analysis (AFA) [electronic only]. 01/2014; 2(2).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we characterize the validity of the Hardytype inequality \begin{equation*} \left\\left\\int_s^{\infty}h(z)dz\right\_{p,u,(0,t)}\right\_{q,w,\infty}\leq c \,\h\_{1,v,\infty} \end{equation*} where $0<p< \infty$, $0<q\leq +\infty$, $u$, $w$ and $v$ are weight functions on $(0,\infty)$. It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces for Hardytype operators restricted to the cone of monotone functions and for the generalized Stieltjes operator.Journal of Inequalities and Applications 11/2013; 2013(515). · 0.82 Impact Factor 
Article: Some scales of equivalent conditions to characterize the Stieltjes inequality: the case q < p
[Show abstract] [Hide abstract]
ABSTRACT: We prove that the weighted Stieltjes inequality ∞ 0 ∞ 0 h(t)dt (x + t) λ q u(x)dx 1/q ≤ C ∞ 0 h p (x)v(x)dx 1/ p can be characterized by four different scales of conditions also for the case 0 < q < p < ∞, 1 < p. In particular, a new proof of a result of G. Sinnamon [10] is given, which also covers the case 0 < q < 1. Moreover, for the situation at hand a new gluing theorem and also an equivalence theorem of independent interest are proved and discussed. By applying our new equivalence theorem to weighted inequalities for the Stieltjes transform we obtain the four new scales of conditions for characterization of Stieltjes inequality. C 2013 WILEYVCH Verlag GmbH & Co. KGaA, WeinheimMathematische Nachrichten 11/2013; · 0.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We study the boundedness of weighted multidimensional Hardytype operators and of variable order , with radial weight , from a variable exponent locally generalized Morrey space to another . The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by , , and , the belongness of which to the resulting space is sufficient for such a boundedness. Under additional assumptions on , this condition is also necessary. We also give the boundedness conditions in terms of Zygmundtype integral inequalities for the functions and .Journal of function spaces and applications 10/2013; 2013. · 0.58 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Let 1 < p ≤ q < ∞. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions.Mathematische Nachrichten 05/2013; 286(7):659 – 668. · 0.66 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we present and discuss some new developments of Hardytype inequalities, namely to derive (a) Hardytype inequalities via a convexity approach, (b) refined scales of Hardytype inequalities with other ``breaking points'' than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardytype inequalities.11/2012;  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we study boundedness of commutators of the multidimensional Hardy type operators with BMO coefficients, in weighted global and/or local generalized Morrey spaces LΠp,J(Rn,w) and vanishing local Morrey spaces VLlocp,J(Rn,w) defined by an almost increasing function J(r) and radial type weight w(x). This study is made in the perspective of posterior applications of the weighted results to some problems in the theory of PDE. We obtain sufficient conditions, in terms of some integral inequalities imposed on J and w, and also in terms of the MatuszewskaOrlicz indices of J and w, for such a boundedness.11/2012;  [Show abstract] [Hide abstract]
ABSTRACT: First we present and discuss an important proof of Hardy's inequality via Jensen's inequality which Hardy and his collaborators did not discover during the 10 years of research until Hardy finally proved his famous inequality in 1925. If Hardy had discovered this proof, it obviously would have changed this prehistory, and in this article the authors argue that this discovery would probably also have changed the dramatic development of Hardy type inequalities in an essential way. In particular, in this article some results concerning powerweight cases in the finite interval case are proved and discussed in this historical perspective. Moreover, a new Hardy type inequality for piecewise constant p = p(x) is proved with this technique, limiting cases are pointed out and put into this frame. Mathematics Subject Classification: 26D15.Journal of Inequalities and Applications 01/2012; 2012(1). · 0.77 Impact Factor 
Article: Some higher order Hardy inequalities
[Show abstract] [Hide abstract]
ABSTRACT: We investigate the kth order Hardy inequality (1.1) for functions satisfying rather general boundary conditions (1.2), show which of these conditions are admissible and derive sufficient, and necessary and sufficient, conditions (for 0 < q < ∞, p > 1) on u, v for (1.1) to hold.Journal of Inequalities and Applications 01/2012; 2012(1). · 0.77 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A weight function w(x) on (0,l) or (l,∞), is said to be quasimonotone if w(x)x a 0 ≤C 0 w(y)y a 0 either for all x≤y or for all y≤x, for some a 0 ∈ℝ, C 0 ≥1. In this paper we discuss, complement and unify several results concerning quasimonotone functions. In particular, some new results concerning the close connection to index numbers and generalized BaryStechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e.g. in interpolation theory, Fourier analysis, Hardytype inequalities, singular operators and homogenization theory.Mathematical Inequalities and Applications 01/2012; 15(3). · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In the context of generalized Orlicz spaces, the products X Φ 1 ⊙X Φ 2 and X Φ 1 ⊗X Φ 2 are studied and conditions are obtained under which these spaces are contained in a suitable space X Φ . These imbedding results (inequalities) are in a sense sharp and for the case X=L 1 , the conditions are even necessary and sufficient. Moreover, a new Hölder type inequality is proved.Mathematical Inequalities and Applications 01/2012; 15(3). · 0.49 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Let be a concave function with . There is a corresponding map for which the inverse Minkowski inequality holds. Several properties of that map are obtained. Also, we consider the BeckenbachDresher type inequality connected with ψdirect sums of Banach spaces and of ordered spaces. In the last section we investigate the properties of functions ψ ω,q and ∥.∥ω,q , (0 < ω < 1, q < 1) related to the Lorentz sequence space. Other posibilities for parameters ω and q are considered, the inverse Holder inequalities and more variants of the BeckenbachDresher inequalities are obtained. 2000 MSC: Primary 26D15; Secondary 46B99.Journal of Inequalities and Applications 01/2012; 2012(1). · 0.77 Impact Factor
Publication Stats
409  Citations  
34.20  Total Impact Points  
Top Journals
Institutions

1997–2013

Luleå University of Technology
 Department of Engineering Sciences and Mathematics
Luleå, Norrbotten, Sweden


2010

University of West Bohemia
Pilsen, Plzeňský, Czech Republic


1997–2004

Lund University
 Division of Mathematics
Lund, Skåne, Sweden
