We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

[1] G. H. HARDY, J. E. LITTLEWOOD AND G. POLYA, Inequalities, Cambridge Univ. Press, Cambridge, 1995. [2] GAO MINGZHE, A Note on the Hardy-Hilbert Inequality, J. Math. Anal. Appl. Vol. 204, No. 1 (1996), 346–351. [3] GAO MINGZHE AND YANG BICHEN, on the Extended Hilbert’s Inequality, Proc. Amer. Math. Soc. Vol. 126, No. 3 (1998), 751–759. [4] W. H. GREUB, Linear Algebra, Springer Verlag, Berlin,...

In the present paper, by introducing some parameters, new forms of Hardy-Hilbert’s inequalities are given.

Hilbert and Hardy-Hilbert type inequalities see 1 are very significant weight inequalities which play an important role in many fields of mathematics. Although classical, such inequalities have attracted the interest of numerous mathematicians and have been generalized in many different ways. Also the numerous mathematicians reproved them using various techniques. Some possibilities of generali...

1. INTRODUCTION. The development of the famous Hardy inequality (in both its discrete and continuous forms) during the period 1906–1928 has its own history or, as we have called it, prehistory. Contributions of mathematicians other than G. are important here. In this article we describe some of those contributions. We also include and comment upon several facts and early proofs that are not ava...

In this paper, we aim to construct $n$ dimensional Jensen, Hardy and Hermite-Hadamard type inequalities for multiple diamond-alpha integral on time scales. The cases of inequality with a weighted function three variables are also considered minutely.

Abstract In this article, we first apply the method of combining interpolation theorem and weak-type estimate developed in Chen et al. to derive Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel. By using weighted Hardy inequality, further obtain Stein-Weiss For extremal problem corresponding presence double-weighted exponents not being necessarily nonnegative makes it impossi...

Making use of weight coefficients as well real/complex analytic methods, an extension a Hardy–Hilbert-type inequality with best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression the norm, few particular cases are also considered.

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...

Although the Hardy inequality corresponding to one quadratic singularity, with optimal constant, does not admit any extremal function, it is well known that such a potential can be improved, in the sense that a positive term can be added to the quadratic singularity without violating the inequality, and even a whole asymptotic expansion can be build, with optimal constants for each term. This p...