English
norskBlar i tittel Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag)
Viser treff 117-136 av 161
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Some Fourier inequalities for orthogonal systems in Lorentz–Zygmund spaces
(Journal article; Peer reviewed, 2019-06-13)A number of classical inequalities and convergence results related to Fourier coefficients with respect to unbounded orthogonal systems are generalized and complemented. All results are given in the case of Lorentz–Zygmund spaces. -
Some inequalities for Cesàro means of double Vilenkin-Fourier series
(Journal article; Peer reviewed; Tidsskriftartikkel, 2018-12-19)In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp. -
Some inequalities related to strong convergence of Riesz logarithmic means
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-23)In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series. -
Some new estimates of the ‘Jensen gap’
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-02-01) -
Some New Fourier and Jackson–Nikol’skii Type Inequalities in Unbounded Orthonormal Systems
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-09-16)We consider the generalized Lorentz space L_ψ,q defined via a continuous and concave function ψ and the Fourier series of a function with respect to an unbounded orthonormal system. Some new Fourier and Jackson-Nikol’skii type inequalities in this frame are stated, proved and discussed. In particular, the derived results generalize and unify several well-known results but also some new applications ... -
Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-03-20)In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces L q,r (logL ) α Lq,r(logL)α involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for ... -
Some new Hardy-type inequalities for Riemann-Liouville fractional q-integral operator
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2015-09-24)We consider the q-analog of the Riemann-Liouville fractional q-integral operator of order n∈Nn∈N. Some new Hardy-type inequalities for this operator are proved and discussed. -
Some new Hardy-type inequalities in q-analysis
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-09)We derive necessary and sufficient conditions (of Muckenhoupt-Bradley type) for the validity of q -analogs of (r, p) -weighted Hardy-type inequalities for all possible positive values of the parameters r and p . We also point out some possibilities to further develop the theory of Hardy-type inequalities in this new direction. -
Some New Iterated Hardy-Type Inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2012-12-10) -
Some new iterated Hardy-type inequalities: the case theta=1
(Journal article; Tidsskriftartikkel; Peer reviewed, 2013-11-08)In this paper we characterize the validity of the Hardy-type inequality ∥ ∥ ∫ <sub>s</sub>∞) h(z)dz ∥ p,u,(0,t) ∥ q,w,(=,∞≤ c∥h∥ 1,v(0,∞) where 0 < p < ∞,0< q ≤ +∞, u, w and v are weight functions on (0,∞). It is pointed out that this characterization can be used to obtain new characterizations for the boundedness between weighted Lebesgue spaces ... -
Some new multidimensional Cochran-Lee and Hardy type inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)A multidimensional Cochran-Lee operator is introduced and investigated in the frame of Hardy-type inequalities with parameters 0<p⩽q<∞. Moreover, for the case p=q and power weights even the sharp constant is derived, thus generalizing the original Cochran-Lee inequality to a multidimensional setting. As applications both several known but also new inequalities are pointed out. -
SOME NEW REFINEMENTS OF HARDY-TYPE INEQUALITIES
(Journal article; Tidsskriftartikkel; Peer reviewed, 2020-02-11)We obtain some further refinements of Hardy-type inequalities via superqudraticity technique. Our results both unify and further generalize several results on refinements of Hardy-type inequalities in the literature. -
Some new refinements of the Young, Hölder, and Minkowski inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-21)We prove and discuss some new refined Hölder inequalities for any p>1 and also a reversed version for 0<p<1. The key is to use the concepts of superquadraticity, strong convexity, and to first prove the corresponding refinements of the Young and reversed Young inequalities. Refinements of the Minkowski and reversed Minkowski inequalities are also given. -
Some new restricted maximal operators of Fejér means of Walsh–Fourier series
(Journal article; Tidsskriftartikkel, 2023-09-12)In this paper, we derive the maximal subspace of natural numbers { <i>n<sub>k</sub></i> : <i>k</i> ≥ 0 }, such that the restricted maximal operator, defined by sup<sub><i>k</i>∈ℕ</sub> | σ<i><sub>n<sub>k</sub></sub>F</i> | on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space <i>H</i><sub>1/2</sub> to the Lebesgue space ... -
Some new Two-Sided Inequalities concerning the Fourier Transform
(Journal article; Peer reviewed; Tidsskriftartikkel, 2017)The classical Hausdorff-Young and Hardy-Littlewood-Stein inequalities do not hold for p > 2. In this paper we prove that if we restrict to net spaces we can even derive a two-sided estimate for all p > 1. In particular, this result generalizes a recent result by Liflyand E. and Tikhonov S. [7] (MR 2464253). -
Some New Weak (Hp- Lp)-Type Inequality for Weighted Maximal Operators of Partial Sums of Walsh–Fourier Series
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-08-18)In this paper, we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space H<sub>p</sub>(G) to the Lebesgue space weak−L<sub>p</sub>(G), for 0<p<1. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known ... -
Some New weak-(Hp-Lp) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-13)We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space H<sub>p</sub>(G) to the space weak-L<sub>p</sub>(G), for 0 <p<1/2. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results. -
Some sharp inequalities for integral operators with homogeneous kernel
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-04-09)One goal of this paper is to show that a big number of inequalities for functions in Lp(R+), p ≥ 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and ... -
Some weak type inequalities and almost everywhere convergence of Vilenkin–Nörlund means
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-05-04)We prove and discuss some new weak type (1, 1) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out. -
Stationary convection-diffusion equation in an infinite cylinder
(Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12-21)We study the existence and uniqueness of a solution to a linear stationary convection–diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of two semi-infinite cylinders with two different periodic regimes. Depending on the direction of the effective convection in the two semi-infinite cylinders, we ...
