Search

The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.

The real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.

The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.

This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality. Applications to function spaces and geometric measures are also presented. This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.

During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.

Drawing on debates from traditional and postmodern thoughts on science and technology, the title builds a new theoretical framework to reconsider science and technology, integrating the opposing viewpoints that either justify science or negate it. As the third volume of a three-volume set that proposes to reconsider science and technology and explores how the philosophy of science and technology responds to an ever-changing world, this final volume seeks to restore the cultural implications of science. Across the six chapters, the authors probe the prospect of a pluralistic scientific culture, including discussions of diversified value choices, the tension between reason and unreason, other binary characteristics of scientific knowledge, including objectivity and uniqueness, universality and locality, as well as the loss, awakening and reconstruction of scientific culture. The authors call for a transformation of scientific culture from a dominant culture to an affirmative one and envision a free and open world of science and technology. The volume will appeal to scholars and students interested in the philosophy of science and technology, the ideology of scientism and anti-scientism, modernism and postmodernism, Marxist philosophy and topics related to scientific culture.

In reviewing and reconsidering the intellectual history of scientism and antiscientism, the authors assess the process of reasoning and prejudices of these contrasting viewpoints, while discussing the repercussions of scientific hegemony and its contemporary criticism. As the second volume of a three-volume set that proposes to reconsider science and technology and explores how the philosophy of science and technology responds to an ever-changing world, this title focuses on ideological trends centering around scientism and anti-scientism since the 19th century. The six chapters look into the emergence of scientism, instrumental reason, scientific optimism, scientific pessimism, scientific crisis and irrationalism and finally the deconstruction of scientism. The authors provide insight into the connections and biases of these disparate views and critiques, explore the influences of the hegemony of science and contemporary critique of science and evaluate the value of postmodernism and deconstructivism. The volume will appeal to scholars and students interested in the philosophy of science and technology, the ideology of scientism and anti-scientism, modernism and postmodernism, Marxist philosophy and topics related to scientific culture.

In reviewing and reconsidering the intellectual history of scientism and antiscientism, the authors assess the process of reasoning and prejudices of these contrasting viewpoints, while discussing the repercussions of scientific hegemony and its contemporary criticism. As the second volume of a three-volume set that proposes to reconsider science and technology and explores how the philosophy of science and technology responds to an ever-changing world, this title focuses on ideological trends centering around scientism and anti-scientism since the 19th century. The six chapters look into the emergence of scientism, instrumental reason, scientific optimism, scientific pessimism, scientific crisis and irrationalism and finally the deconstruction of scientism. The authors provide insight into the connections and biases of these disparate views and critiques, explore the influences of the hegemony of science and contemporary critique of science and evaluate the value of postmodernism and deconstructivism. The volume will appeal to scholars and students interested in the philosophy of science and technology, the ideology of scientism and anti-scientism, modernism and postmodernism, Marxist philosophy and topics related to scientific culture.