👉 Holder's math is a branch of mathematics that focuses on the properties and behaviors of functions defined on metric spaces, particularly those with a rich geometric structure. It extends classical functional analysis by considering operators and functions on spaces that may not be normed or complete, such as Banach spaces or locally compact Hausdorff spaces. Holder's theorem, a cornerstone of this field, provides conditions under which certain operators, known as Hölder continuous functions, are bounded between two given spaces. This is crucial for understanding the continuity and integrability of functions in various contexts, including partial differential equations and harmonic analysis. The theory is named after Otto Holder, who first introduced these concepts in the early 20th century.
