Starting with the fundamentals of Q spaces and their relationships to Besov spaces, this book presents all major results around Q spaces obtained in the past 16 years. The applications of Q spaces in the study of the incompressible Navier-Stokes system and its stationary form are also discussed. This self-contained book can be used as an essential reference for researchers and graduates in analysis and partial differential equations.

This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.

This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.

This book covers the latest developments and advances in spray drying and describes how they impact the basic aspect of designing and operating spray dryers. This generic approach allows users to understand how different basic aspects of spray drying have advanced. Users will learn how to apply these advances in their own specific spray drying applications. This book also discusses the handling and control of spray dried products. Includes the latest techniques for use in the design and operation of spray drying operations Covers the basic operations of spray drying that can be applied to different applications of spray drying Discusses the handling and control of spray dried product qualities from a general approach, allowing readers to tailor these approaches to their own specific products This book is aimed at professionals, researchers, and academics working in the fields of food, chemical, pharmaceutical, and industrial engineering.

This book covers the latest developments and advances in spray drying and describes how they impact the basic aspect of designing and operating spray dryers. This generic approach allows users to understand how different basic aspects of spray drying have advanced. Users will learn how to apply these advances in their own specific spray drying applications. This book also discusses the handling and control of spray dried products. Includes the latest techniques for use in the design and operation of spray drying operations Covers the basic operations of spray drying that can be applied to different applications of spray drying Discusses the handling and control of spray dried product qualities from a general approach, allowing readers to tailor these approaches to their own specific products This book is aimed at professionals, researchers, and academics working in the fields of food, chemical, pharmaceutical, and industrial engineering.

This book documents the rich structure of the holomorphic Q function spaces which are geometric in the sense that they transform naturally under conformal mappings, with particular emphasis on recent development based on interaction between geometric function and measure theory and other branches of mathematical analysis, including potential theory, harmonic analysis, functional analysis, and operator theory. Largely self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces. Self-contained, the book functions as an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.

The space Q p consists of all holomorphic functions f on the unit disk for which the L^2 area integrals of its derivative against the p-th power of the Green function of the unit disk are uniformly bounded in the variable that survives the integration. It turns out that Q 1 coincides with BMOA, while, for p>1, Q p are just the Bloch space. For p/in (0,1) the Q p furnish an increasing sequence of spaces, each invariant under conformal mappings of the unit disk onto itself, which interpolate between the Dirichlet space and BMOA. This monograph covers a number of important aspects in complex, functional and harmonic analysis. The primary focus is Q p, p/in (0,1), and their equivalent characterizations. Based on the up-to-date results obtained by experts in their respective fields, each of the eight chapters unfolds from the basics to the more complex. The exposition here is rapid-paced and efficient, with proofs and examples.

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 Poincare 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.