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Now showing items 1-10 of 17

#### 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 ...

#### On Weighted Fourier InequalitieS –– Some New Scales of Equivalent Conditions

(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-06)

For Lebesgue spaces on R<sup>n</sup>, we study two-weight p → q-inequalities for Fourier
transform. Some sufficient conditions on weights for such inequalities are known for special
ranges of parameters p and q. In the same ranges of parameters we show, that in every case each
of those conditions can be replaced by infinitely many conditions, even by continuous scales of
conditions. We also ...

#### Weighted Hardy Operators in Complementary Morrey Spaces

(Journal article; Tidsskriftartikkel; Peer reviewed, 2012-11-11)

We study the weighted -boundedness of the multidimensional weighted Hardy-type operators and with radial type weight , in the generalized complementary Morrey spaces defined by an almost increasing function . We prove a theorem which provides conditions, in terms of some integral inequalities imposed on and , for such a boundedness. These conditions are sufficient in the general case, but we ...

#### Continuous refinements of some Jensen-type inequalities via strong convexity with applications

(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-05-23)

In this paper we prove new continuous refinements of some Jensen type inequalities
in both direct and reversed forms. As applications we also derive some continuous
refinements of Hermite–Hadamard, Hölder, and Popoviciu type inequalities. As
particular cases we point out the corresponding results for sums and integrals
showing that our results contain both several well-known but also some new ...

#### Refinements of some classical inequalities via superquadraticity

(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-06-21)

Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are
stated and proved. In particular, these results both generalize and unify several results
of this type. Some results are also new for the classical situation.

#### Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods

(Journal article; Tidsskriftartikkel; Peer reviewed, 2022-09-17)

The concept of Vilenkin–Lebesgue points was introduced in
[12], where the almost everywhere convergence of Fejer means of
Vilenkin–Fourier series was proved. In this paper, we present a different
(and simpler) approach to prove a similar result, which can be used to
prove that the corresponding result holds also in a more general context,
namely for regular Norlund and T-means.

#### 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.

#### 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.

#### (Hp− Lp -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series

(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-04-07)

#### On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus

(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-01-19)

In this paper, we explore a generalised solution of the Cauchy problems for the q-heat and q-wave equations which are generated
by Jackson’s and the q-Sturm-Liouville operators with respect to t and x, respectively. For this, we use a new method, where a
crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show
that these solutions ...