A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions

• Autorzy: Michael Cwikel , Yoram Sagher , Pavel Shvartsman
• Języki publikacji: EN

Abstrakty

EN

The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs of the celebrated John-Nirenberg inequality and of related inequalities due to John and to Wik. One of our main results is that an affirmative answer to the above question would lead to a version of the John-Nirenberg inequality with "dimension free" constants.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 95
• Numer: 1
• Strony: 45-53

Daty

wydano

2011

Twórcy

autor

Michael Cwikel

• Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

autor

Yoram Sagher

• Department of Mathematics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA

autor

Pavel Shvartsman

• Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

Identyfikatory

DOI

10.4064/bc95-0-3