Classes of Hardy spaces associated with operators, duality theorem and applications

By Lixin Yan. 2008

101 citations recorded by the source corpus.

Let L be the infinitesimal generator of an analytic semigroup on L 2 (R n ) with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space H1 L(R n ) and a BMO L (R n ) space associated with the operator L were introduced and studied. In this paper we define a class of H p L (R n ) spaces associated with the operator L for a range of p < 1 acting on certain spaces of Morrey-Campanato functions defined in New Morrey-Campanato spaces associated with operators and applications by Duong and Yan (2005), and they generalize the classical H p (R n ) spaces. We then establish a duality theorem between the H p L (R n ) spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on H p L (R n ) and give the inclusion between the classical H p (R n ) spaces and the H p L (R n ) spaces associated with operators.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fa795d9fb69fe4953b6560aa285449c0e155883a

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In Applied Mathematics

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

In Mathematical Physics

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

Citations in the corpus

• 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.”
• 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 H1L(R n) is just BMOL∗(R n), where L∗ denotes the adjoint operator of L in L2(Rn).”
• Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010, background): “Beside s th aforementioned works [11] and [40], some properties of the Hardy and BMO spaces associated with different operators were introduced previously in [ 12], [26], [27], [61].”
• Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates (2009, background): “Yan [33] further generalized these results to the Hardy space H L(R n) with p ∈ (0, 1] close to 1 and its dual space.”
• Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus☆ (2013, background): “In recent years, function spaces, especially Hardy spaces and BMO spaces, associated with operators have been studied extensively; see, for example, [4], [6], [7], [15], [17], [18], [20], [21], [37] and references therein.”
• Orlicz-Hardy spaces associated with operators (2009, methodology): “Duong and Yan [5, 6, 11] and Yan [ 10 ] introduced the BMO and Morrey-Campanato spaces associated with L. Motivated by this, in what follows, we introduce the space BMO q, s”