Impact of Congenital Heart Disease at Adulthood

Since the first surgical techniques for patients with congenital heart disease (ConHD) became available some 55 years ago, virtually every area of patient care has evolved substantially. These improvements lead to an increased survival for patients with ConHD, with over 90% of infants reaching adulthood. This increased survival lead to a shift of focus in that congenital heart disease at adult age nowadays is considered a chronic disease. Therefore, current research does not only focus on survival, but also on the quality of life of these patients. The term quality of life is broad and encompasses many dimensions of life, including – but not limited to – living conditions, wealth and employment, physical and mental health, education, leisure time, psychosocial functioning, lifestyle and social adaptation. In order to investigate the impact of living with a congenital heart defect at adulthood, the aims of this thesis were threefold; 1) To investigate the impact on biographical characteristics 2) To investigate the impact on psychological aspects 3) To investigate the impact on medical aspect

Sharp Embeddings of Besov Spaces with Logarithmic Smoothness

Sin resume

Sharp embeddings of Besov spaces involving only slowly varying smoothness

AS CRGRICES201/05/2033201/08/0383Grant Agency of the CzechInstitutional Research Plan no. AV0Z10190503 of theFCT05-1000008-815

Optimal embeddings and compact embeddings of Bessel-potential-type spaces

First, we establish necessary and sufficient conditions for embeddings of Bessel potential spaces H^ σ X(R^n) with order of smoothness less than one, modelled upon rearrangement invariant Banach function spaces X(R^n), into generalized Hölder spaces. To this end, we derive a sharp estimate of modulus of smoothness of the convolution of a function f in X(R^n) with the Bessel potential kernel gσ , 0 < s < 1. Such an estimate states that if gσ belongs to the associate space of X, then ω(f* gσ,t) precsim \int\limits_0^{t^n}s^{\frac{\σ}{n}-1}f^*(s)\,ds \quad {\rm for\,all} \quad t\in(0,1) \quad {\rm and\,every}\quad f in X(R^n). Second, we characterize compact subsets of generalized Hölder spaces and then we derive necessary and sufficient conditions for compact embeddings of Bessel potential spaces Hσ X(R^n) into generalized Hölder spaces. We apply our results to the case when X(R^n) is the Lorentz–Karamata space {L_{p,q;b}(R^n)}. In particular, we are able to characterize optimal embeddings of Bessel potential spaces {H^{σ}L_{p,q;b}(R^n)} into generalized Hölder spaces and also compact embeddings of spaces in question. Applications cover both superlimiting and limiting cases

A unified approach to inequalities for K-functionals and moduli of smoothness

The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified approach based on Holmstedt formulas to obtain these estimates. As examples, we derive new inequalities for moduli of smoothness and K-functionals in various Lorentz spaces