Why do you think your paper is highly cited?

In recent decades, there has been a growing interest in the study of weighted composition operators on spaces of holomorphic functions, which are denoted by uC_p and also in providing function-theoretic characterizations when the functions u and p induce bounded or compact weighted composition operators between spaces of holomorphic functions.

Usually, some necessary and sufficient conditions for the operator to be bounded or compact are given, sometimes with an asymptotic formula for its operator norm. In this short note, we managed to calculate the norm of the weighted composition operator from the Bloch space to a weighted-type space on the unit ball. The problem of calculating operator norms is a basic one but usually quite difficult. There are not many papers which contain such results. This is one of the reasons why my paper is of particular interest.

Does it describe a new discovery, methodology, or synthesis of knowledge?

Working on Bloch-type spaces, I've realized that sometimes it is useful to use the norm on the space by taking radial derivatives, while in some other cases it's better to use the norm containing the gradient of the functions in the space—as in the current paper.

In calculating operator norms of weighted composition operators, it turned out that it is important to obtain an exact estimate for the point evaluation operator, for getting an estimate of the operator norm from above and in choosing some test functions which have growth approximately equal to the estimate, to obtain an estimate of the operator norm from below. This need not lead to one's getting a formula for operator norm of a weighted composition operator, but it does offer a method which can be considered useful.

Would you summarize the significance of your paper in layman's terms?

This paper reestablished interest in an area not only connected to weighted composition operators, but also to other operators on spaces of holomorphic functions. The method seems fruitful indeed. For example, in my recent paper: "Norms of some operators from Bergman spaces to weighted and Bloch-type space," Util. Math. 76: 59-64, 2008, among others, I calculated the norm of some integral-type operators, while in "Norm and essential norm of composition followed by differentiation from a-Bloch spaces to ," Appl. Math. Comput. 207: 225-29, 2009, I calculated the norm of composition followed by differentiation operator from the Bloch and the little Bloch space to a weighted-type space on the unit disk and gave an upper and a lower bound for the essential norm of the operator from the a-Bloch space to .

How did you become involved in this research, and were there any problems along the way?

The main result in my paper was motivated by the results shown in my article entitled: "Weighted composition operators between H(infinity) and a -Bloch spaces in the unit ball" Taiwanese J. Math. 12: 1625-39, 2008, and is a kind of addendum to it. I had initially hesitated to publish the note because of its brevity, but in a private communication with several experts, I realized that it could actually be quite interesting.

In general, I first became involved in this theory about 10 years ago by reading papers on the research area as published in several journals. It is well-known that I'm a self-taught mathematician and, having been on my own, I was simply looking for areas which could be of special interest to me. I then came across several fascinating articles on the subject of composition operators, and this led to my examination of the field.

Where do you see your research leading in the future?

There are many interesting areas in mathematics and it is well known that I've published papers across several quite different fields, so it's difficult to predict which direction may prevail in my future research. I will certainly continue to study systematically the properties of various operators on the spaces of holomorphic functions.

Recently, I introduced several new integral-type operators which have already attracted some attention and I will continue to study recent types of nonlinear difference equations, which are not closely connected to differential equations, such as, rational and max-type difference equations. I am also interested in equations which model some real-life situations.

Stevo Stevic
Mathematical Institute of the Serbian Academy of Sciences
Belgrade, Serbia

KEYWORDS: BERGMAN-TYPE SPACES; H-INFINITY; POLYDISK.