A Tale of Three Platforms: Investigating Preschoolers’ Second-Order Inferences Using In-Person, Zoom, and Lookit Methodologies

As a result of the COVID-19 pandemic, online methodologies for developmental research have become an essential norm. Already, there are numerous options for recruiting and testing developmental participants, and they differ from each other in a variety of ways. While recent research has discussed the potential benefits and practical trade-offs of these different platforms, the potential empirical consequences of choosing among them are still unknown. It is critical for the field to understand not only how children’s performance in an online context compares to traditional settings, but also how it differs across online platforms. This study offers the first comparative look at the same developmental task across different online research methodologies, allowing for direct comparison and critical examination of each. We conducted three versions of a test of preschoolers’ ability to generate and apply second-order inferences to predict novel outcomes. Experiment 1 is an in-person task conducted at public testing sites in the vicinity of the university. In Experiment 2, we conducted an online-moderated version of the same task, in which an experimenter presented a recording of the procedure during a live video call with families over Zoom. Finally, Experiment 3 is an online-unmoderated version of the task, in which the same videos were presented entirely asynchronously using the Lookit platform. Results suggest that online methodologies may introduce difficulties and age-related differences in young children’s performance not observed in person. We consider these results in light of the previous online developmental replications, suggest possible interpretations, and offer initial recommendations to help future developmental scientists make informed choices about whether and how to conduct their research online.

Compact Hankel Operators Between Distinct Hardy Spaces and Commutators

The paper is devoted to the study of compactness of Hankel operators acting between distinct Hardy spaces generated by Banach function lattices. We prove an analogue of Hartman’s theorem characterizing compact Hankel operators in terms of properties of their symbols. As a byproduct we give an estimation of the essential norm of such operators. Furthermore, compactness of commutators and semicommutators of Toeplitz operators for unbounded symbols is discussed.

New characterizations for differences of composition operators between weighted-type spaces in the unit ball

In this paper, we present some asymptotically equivalent expressions to the essential norm of differences of composition operators acting on weighted-type spaces of holomorphic functions in the unit ball of . Especially, the descriptions in terms of are described. From which the sufficient and necessary conditions of compactness follows immediately. Also, we characterize the boundedness of these operators.

The Product-Type Operators from Hardy Spaces into n th Weighted-Type Spaces

The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators T u , v , φ m , m ∈ ℕ from Hardy spaces into n th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators.

EQUIVALENCE OF SEMI-NORMS RELATED TO SUPER WEAKLY COMPACT OPERATORS

We study super weakly compact operators through a quantitative method. We introduce a semi-norm $\sigma (T)$ of an operator $T:X\to Y$ , where X, Y are Banach spaces, the so-called measure of super weak noncompactness, which measures how far T is from the family of super weakly compact operators. We study the equivalence of the measure $\sigma (T)$ and the super weak essential norm of T. We prove that Y has the super weakly compact approximation property if and and only if these two semi-norms are equivalent. As an application, we construct an example to show that the measures of T and its dual $T^*$ are not always equivalent. In addition we give some sequence spaces as examples of Banach spaces having the super weakly compact approximation property.

Weighted Composition Operators from Derivative Hardy Spaces into n -th Weighted-Type Spaces

The boundedness, compactness, and the essential norm of weighted composition operators from derivative Hardy spaces into n -th weighted-type spaces are investigated in this paper.

Embedding of Besov Spaces and the Volterra Integral Operator

The boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces are studied in this paper. Meanwhile, the boundedness, compactness, and essential norm of the Volterra integral operator T g from Besov spaces to a class of general function spaces are also investigated.

The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.