Related papers: Some characterizations of slice regular Lipschitz …
Given a quaternionic slice regular function $f$, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the…
This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum modulus principle will be generalized to our setting. Some…
The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen's prediction of characteristic numbers of smooth plane…
In the setting of $\R^d$ with an $n-$dimensional measure $\mu,$ we give several characterizations of Lipschitz spaces in terms of mean oscillations involving $\mu.$ We also show that Lipschitz spaces are preserved by those Calderon-Zygmund…
The regular subspaces of a Dirichlet form are the regular Dirichlet forms that inherit the original form but possess smaller domains. The two problems we are concerned are: (1) the existence of regular subspaces of a fixed Dirichlet form,…
We study the continuity regularity of functions in the complex Sobolev spaces. As applications, we obtain Hermitian generalizations of a recent result due Guedj-Guenancia-Zeriahi on the diameters of Kaehler metrics.
In this paper we introduce the notion of slice regular right linear semigroup in a quaternionic Banach space. It is an operatorial function which is slice regular (a noncommutative counterpart of analyticity) and which satisfies a…
This paper studies NET map slope functions. It establishes Lipschitz-type conditions for them. It relates Lipschitz-type conditions to the half-space theorem. It gives bounds on the number of slope function fixed points. It provides…
In the article the class of slice regular functions is shown to be closed under a new regular composition. The new regular composition turns out to be globally defined in contrast to the locally defined version by Vlacci. Its advantage over…
The regular fractional transformations of the extended quaternionic space have been recently introduced as variants of the classical linear fractional transformations. These variants have the advantage of being included in the class of…
We investigate several boundedness properties of function spaces considered as uniform spaces.
In this paper, we establish a three circles type theorem, involving the harmonic area function, for harmonic mappings. Also, we give bounds for length and area distortion for harmonic quasiconformal mappings. Finally, we will study certain…
We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…
The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…
The article examines nonisotropic Nikolskii and Besov spaces with norms defined using $L_p$-averaged moduli of continuity of functions of appropriate orders along the coordinate directions, instead of moduli of continuity of known orders…
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice…
The piecewise-concave function may be used to approximate a wide range of other functions to arbitrary precision over a bounded set. In this short paper, this property is proven for three function classes: (a) the multivariate twice…
In this paper, we introduce a Helmholtz-type decomposition for the space of square integrable, symmetric-matrix-valued functions analogous to the standard Helmholtz decomposition for vector fields. This decomposition provides a better…
In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some…