Related papers: On the equivalence between moderate growth-type co…
We continue the study of the known equivalent reformulations of the classical moderate growth condition for weight sequences in the mixed setting; i.e. when dealing with two different sequences. This approach is becoming crucial in the…
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…
We introduce the new notion of a conjugate weight function and provide a detailed study of this operation and its properties. Then we apply this knowledge to study classes of ultradifferentiable functions defined in terms of fast growing…
We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case…
The aim of this article is to provide characterizations for subadditivity-like growth conditions for the so-called associated weight functions in terms of the defning weight sequence. Such growth requirements arise frequently in the…
We prove in a uniform way that all ultradifferentiable function classes of Roumieu- and of Beurling-type defined in terms of a weight matrix admit a convenient setting if the matrix satisfies some mild regularity conditions. We prove that…
We characterize the inclusion relations between weighted classes of entire functions with rapid decreasing growth and study strong growth comparison relations between given weights. In our considerations first we focus on weights defined in…
The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results…
We study classes of ultradifferentiable functions defined in terms of small weight sequences violating standard growth and regularity requirements. First, we show that such classes can be viewed as weighted spaces of entire functions for…
We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipovi\'c, N. Teofanov and F. Tomi\'c are special cases of the general framework of spaces of ultradifferentiable functions defined in…
We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J.…
In the theory of nonlinear partial differential equations we need to explain superposition operators. For modulation spaces equipped with particular ultradifferentiable weights this was done in \cite{rrs}. In this paper we introduce a class…
A plethora of spaces in Functional Analysis (Braun-Meise-Taylor and Carleman ultradifferentiable and ultraholomorphic classes; Orlicz, Besov, Lipschitz, Lebesque spaces, to cite the main ones) are defined by means of a weighted structure,…
In this paper we extend the theory of two weight, $A_p$ bump conditions to the setting of matrix weights. We prove two matrix weight inequalities for fractional maximal operators, fractional and singular integrals, sparse operators and…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
It is well known that if a finite order linear differential operator with polynomial coefficients has as eigenfunctions a sequence of orthogonal polynomials with respect to a positive measure (with support in the real line), then its order…
We introduce and study new transformations between two functions satisfying some basic growth properties and generalize the known lower and upper Legendre conjugate (or envelope). We also investigate how these transformations modify…
Let $e^{-tL}$ be a analytic semigroup generated by $-L$, where $L$ is a non-negative self-adjoint operator on $L^2(\mathbb{R}^d)$. Assume that the kernels of $e^{-tL}$, denoted by $p_t(x,y)$, only satisfy the upper bound: for all $N>0$,…
We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…
We prove that functions with compact support in non-quasianalytic classes of Roumieu-type and of Beurling-type defined by a weight matrix with some mild regularity conditions can be characterized by the decay properties of their Fourier…