By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions are also considered.

We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting question...

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

In this article, we investigate, a certain localised version of the single-valued extension property for a bounded linear operator on a Banach space. We show that this condition behaves canonically under the Riesz functional calculus, and derive a number of characterisations in terms of kernel-type and range-type spaces for the operator and its adjoint. The theory is exemplified in the case of ...

In this paper it is shown that a new Hardy-Hilbert type integral inequality can be established by introducing a proper integral kernel function, and that the constant factor is proved to be the best possible. In particular, for case p = 2, a new Hilbert type integral inequality is given .And as the mathematics aesthetics, several important constants π and Euler number En appear simultaneously i...

Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...

The principal objects of study in this thesis are the noncommutative Hardy algebras introduced by Muhly and Solel in 2004, also called simply “Hardy algebras,” and their quotients by ultraweakly closed ideals. The Hardy algebras form a class of nonselfadjoint dual operator algebras that generalize the classical Hardy algebra, the noncommutative analytic Toeplitz algebras introduced by Popescu i...

*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...