New function spaces of BMO type, the John‐Nirenberg inequality, interpolation, and applications

By Xuan Thinh Duong, Lixin Yan. 2005

258 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91731a9054e94e1f12558c96ce6faaff564b70d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dachun Yang
2. Xuan Thinh Duong
3. Lixin Yan
4. Sibei Yang
5. Renjin Jiang
6. S. Hofmann
7. Yuan Zhou
8. P. Auscher

In Mathematical Physics

1. Dachun Yang
2. Xuan Thinh Duong
3. Sibei Yang
4. Renjin Jiang
5. S. Hofmann
6. Javier Parcet
7. Lixin Yan
8. P. Auscher

Citations in the corpus

• H1 and BMO for certain locally doubling metric measures spaces (2009, result): “We also mention recent works of X.T. Duong and L. Yan [19, 20], who define a Hardy space H 1 and a space BM O of bounded mean oscillation associated to a given operator satisfying suitable estimates.”
• Old and New Morrey Spaces with Heat Kernel Bounds (2007, methodology): “The second aim is to use those new characterizations as motives of a continuous study of [1, 7 , 5, 9] and so to introduce new Morrey spaces L p,λ (R n ) associated with operators.”
• Hardy Spaces Associated to Non-Negative Self-Adjoint Operators Satisfying Davies-Gaffney Estimates (2011, background): “We conclude this introduction by remarking that this work, as well as the earlier cited papers [ DY1 ], [DY2], [AMR], and [HM], can in some sense be viewed as a companion to the Lp theory developed for general classes of”
• New Abstract Hardy Spaces (2007, background): “and there has been recently a number of works with goal to define an adapted Hardy space [1, 2, 8, 20, 17, 19, 21, 18 , 22, 27].”
• COMPARISON OF THE CLASSICAL BMO WITH THE BMO SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS (2006, methodology): “Indeed, the following result is proved in [16] (Theorem 6.”
• New Orlicz–Hardy spaces associated with divergence form elliptic operators (2009, background): “In this section, we recall some notions and notation on the divergence form elliptic operator, and present some basic properties on Orlicz functions and also describe some basic assumptions on them.”
• Calderón reproducing formulas and new Besov spaces associated with operators (2012, methodology): “We will develop the theme in the works [17,18,1,2] and define the Besov norm Ḃ p,q via quadratic norms of L.”
• Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains (2005, methodology): “Note that we use L(2)loc(R ) instead of the space L(1)loc(R ) as in [19] and [16] since this gives the appropriate setting for the duality between H(1) L and BMOL.”
• Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “Based on this, Duong and Yan [36, 37] introduced the BMO-type space BMOL(R n) associated with L and proved that the dual space of H1 L(R n) is just BMOL∗(R n), where L∗ denotes the adjoint operator of L in L2(Rn).”
• A characterization of the Morrey-Campanato spaces (2005, methodology): “. For every 1 ≤ q DY ].”
• Smooth Fourier multipliers on group von Neumann algebras (2010, background): “Duong and Yan [10, 11] —see also [1, 20]— extended it to certain semigroups of positive maps, but still imposing the existence of a metric in the underlying space, something that a priori we do not have at our disposal.”
• Orlicz-Hardy spaces associated with operators (2009, methodology): “(ii) If ρ ≡ 1, q ∈ [1, ∞ )a nds =0 , then BMO q, s ρ, L (R n ) is just the space BMOL(R n ) introduced by Duong and Yan [ 5 , 6] .I fα ∈ (0 ,θ (L)/n )a ndρ(t )= t α ,t hen BMO q, s ρ, L (R”
• Endpoint estimates for Riesz transforms of magnetic Schrödinger operators (2006, background): “A and related topics, we refer to [1], [ 10 ] and [11].”