we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

We study various inequalities for numerical radius and Berezin number of a bounded linear operator on Hilbert space. It is proved that the pure two-isometry 1 Crawford 0. In particular, we show any scalar-valued non-constant inner function θ, Toeplitz Tθ Hardy space 0, respectively. also shown multiplicative class isometries sub-multiplicative commutants shift. have illustrated these results wi...

New inequalities concerning functions of the form f (xy) similar to Hardy-Hilbert’s integral inequality are presented. A new class of functions denoted by (p, q)−-Hö(I) is defined. Many other new inequalities are also given.

Considering functions f on Rn for which both f and f̂ are bounded by the Gaussian e 1 2 a|x| , 0 < a < 1 we show that their Fourier-Hermite coefficients have exponential decay. Optimal decay is obtained for O(n)−finite functions thus extending the one dimensional result of Vemuri [11].

The paper discusses weighted Hardy type inequalities for a certain class of Volterra integral operators with kernels. Criteria the validity presented are found, which different from criteria obtained earlier.

This paper is a response to an article [26] recently published in Journal of Physics A: Mathematical and Theoretical. The article claims that the theory of resonances and decaying states based on certain rigged Hilbert spaces of Hardy functions is physically untenable. In this paper we show that all of the key conclusions of [26] are the result of either the errors in mathematical reasoning or ...