Extrapolation of Compactness on Banach Function Spaces

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator T in the weighted Lebesgue scale and the compactness of T in the unweighted Lebesgue scale yields compactness of T on a very general class of...

Banach function spaces done right

In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove versions of well-known basic properties of Banach function spaces in the setting of quasi-Banach function...

On the trace embedding and its applications to evolution equations

In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity...

Sparse domination implies vector-valued sparse domination

We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition is characterized by the boundedness of the multisublinear Hardy-Littlewood maximal operator and goes...

A Fuglede type theorem for Fourier multiplier operators

Let E be a translation invariant Banach function space over an infinite compact abelian group G and M_φ be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection invariant (which ensures that φ̄ is also a multiplier symbol for E). The following Fuglede type...

Computational Design of Indoor Arenas (CDIA): Integrating multi-functional spaces and long-span roof structures

Indoor arenas are important public buildings catering for various activities (e.g., sports events, stage performances, assemblies, exhibitions, and daily sports for the public) and serving as landmarks in urban contexts. The multi-functional space and long-span roof structure of an indoor arena are highly interrelated, which impact the multi...

Vector-valued harmonic analysis with applications to SPDE

In this dissertation we develop vector-valued harmonic analysis methods. Particular emphasis is put on the study of stochastic singular integral operators, which arise naturally in the study of SPDE.

Sharp Estimates and Extrapolation for Multilinear Weight Classes

The subject of this thesis is the study of the multilinear Muckenhoupt weight classes and the quantitative boundedness of operators with respect to these weights in both the scalar-valued and the vector-valued setting. This includes the study of multisublinear Hardy-Littlewood maximal operators, sparse forms, and multilinear Rubio de Francia...

Vector-Valued Extensions of Operators Through Multilinear Limited Range Extrapolation

We give an extension of Rubio de Francia’s extrapolation theorem for functions taking values in UMD Banach function spaces to the multilinear limited range setting. In particular we show how boundedness of an m-(sub)linear operator T:Lp1(w1p1)×⋯×Lpm(wmpm)→Lp(wp) for a certain class of Muckenhoupt weights yields an extension of the operator...

The ℓ ^s-boundedness of a family of integral operators on UMD banach function spaces

We prove the ℓ^s-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the ℓ^s-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a...

Rescaled extrapolation for vector-valued functions

We extend Rubio de Francia's extrapolation theorem for functions valued in UMD Banach function spaces, leading to short proofs of some new and known results. In particular we prove Littlewood-Paley-Rubio de Francia-type estimates and boundedness of variational Carleson operators for Banach function spaces with UMD concavifications.

Integrating multi-functional space and long-span structure in the early design stage of indoor sports arenas by using parametric modelling and multi-objective optimization

Indoor multi-functional sports arenas are a complex building type. Integration of the (multi-) functional space and of the large-span structure of the roof mainly determines the overall geometry of the building, and is one of the most challenging phases of the design. Several interdisciplinary numeric assessments and numerous solutions with...

Pointwise Properties of Martingales with Values in Banach Function Spaces

In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new Burkholder–Davis–Gundy type inequality is obtained.

Integrating the Multi-Functional Space and Long-Span Structure for Sports Arena Design: A design exploration process based on design optimization and self-organizing map

The multi-functional space of sports arena is highly related to the long-span structure. To support the integration of these two aspects, design optimization combining parametric modeling, performance simulations, and searching algorithm can be used. However, optimization is powerful in dealing with quantitative performance, but for some soft...

A Parametric Modelling Process for the Integration of Architecture and Structure in Large Multi-functional Sports Hall Design: a Case Study

The integration of architectural (functional spaces) and structural design is especially crucial for the conceptual design of large multi-functional sports halls, due to the strict regulations for functional spaces, the requirement of large-span structure, and the complex interrelationships between these two aspects. This on-going research aims...

Noncommutative and vector-valued Rosenthal inequalities

This thesis is dedicated to the study of a class of probabilistic inequalities, called Rosenthal inequalities. These inequalities provide two-sided estimates for the p-th moments of the sum of a sequence of independent, mean zero random variables in terms of a suitable norm on the sequence itself. Rosenthal inequalities are named after H.P....

Compactness in vector-valued banach function spaces