English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

An important connection between the finite dimensional Gaussian Wick products and\udLebesgue convolution products will be proven first. Then this connection will be used\udto prove an important H¨older inequality for the norms of Gaussian Wick products,\udreprove Nelson hypercontractivity inequality, and prove a more general inequality whose\udmarginal cases are the H¨older and Nelson inequalities mentioned before. We will show\udthat there is a deep connection between the Gaussian H¨older inequality and classic\udHo¨lder inequality, between the Nelson hypercontractivity and classic Young inequality\udwith the sharp constant, and between the third more general inequality and an extension\udby Lieb of the Young inequality with the best constant. Since the Gaussian probability\udmeasure exists even in the infinite dimensional case, the above three inequalities can be\udextended, via a classic Fatou’s lemma argument, to the infinite dimensional framework

A HÖLDER–YOUNG–LIEB INEQUALITY FOR NORMS OF GAUSSIAN WICK PRODUCTS