English
norskBlar i tittel Artikler, rapporter og annet (datateknologi og beregningsorienterte ingeniørfag)
Viser treff 110-129 av 160
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A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces
(Journal article; Peer reviewed, 2018-09-20)The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense. -
Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2016-10-01)We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out. -
Sharpness of some Hardy-type inequalities
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-04)The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure dx with the Haar measure . There are also derived some new two-sided Hardy-type inequalities for monotone functions, where not only the two constants are sharp but also the involved function spaces are ... -
Shock Tube. Detail overview of equipment and instruments in the shock tube experimental setup
(Book; Bok, 2015)The shock tube is a device in which a normal shock wave is produced by the interaction of fluids at significantly high-pressure difference. The shock tube is comprised of two sections known as driver and driven sections. These two sections are interacted with the high-speed valve or a bursting disc. When the interaction happens, a shock wave forms almost instantaneously and propagates into the driven ... -
Singularly perturbed spectral problems in a thin cylinder with fourier conditions on its bases
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019)The paper deals with the bottom of the spectrum of a singularly perturbed second order elliptic operator defined in a thin cylinder and having locally periodic coefficients in the longitudinal direction. We impose a homogeneous Neumann boundary condition on the lateral surface of the cylinder and a generic homogeneous Fourier condition at its bases. We then show that the asymptotic behavior of the ... -
Singularly perturbed spectral problems with Neumann boundary conditions
(Peer reviewed; Journal article; Tidsskriftsartikkel, 2015-09-07)The paper deals with the Neumann spectral problem for a singularly perturbed second-order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue and eigenfunction. Using the logarithmic transformation, we reduce the studied problem to an additive eigenvalue problem for a singularly perturbed Hamilton–Jacobi ... -
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 ...
