## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 10, Number 2 (2016), 320-337.

### Multiple Hilbert-type inequalities involving some differential operators

Vandanjav Adiyasuren, Tserendorj Batbold, and Mario Krnić

#### Abstract

In this article, we derive several multidimensional Hilbert-type inequalities, including certain differential operators. Further, we determine the conditions under which the constants appearing on the right-hand sides of the established inequalities are the best possible. As an application, some particular examples are also studied.

#### Article information

**Source**

Banach J. Math. Anal., Volume 10, Number 2 (2016), 320-337.

**Dates**

Received: 6 April 2015

Accepted: 10 June 2015

First available in Project Euclid: 4 April 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1459772692

**Digital Object Identifier**

doi:10.1215/17358787-3495561

**Mathematical Reviews number (MathSciNet)**

MR3481107

**Zentralblatt MATH identifier**

1337.26027

**Subjects**

Primary: 26D10: Inequalities involving derivatives and differential and integral operators

Secondary: 33B15: Gamma, beta and polygamma functions

**Keywords**

Hilbert-type inequality Hardy inequality differential operator best constant

#### Citation

Adiyasuren, Vandanjav; Batbold, Tserendorj; Krnić, Mario. Multiple Hilbert-type inequalities involving some differential operators. Banach J. Math. Anal. 10 (2016), no. 2, 320--337. doi:10.1215/17358787-3495561. https://projecteuclid.org/euclid.bjma/1459772692