Hardy bmo space
In analysis on the real vector space R , the Hardy space H (for 0 < p ≤ ∞) consists of tempered distributions f such that for some Schwartz function Φ with ∫Φ = 1, the maximal function is in L (R ), where ∗ is convolution and Φt (x) = t Φ(x / t). The H -quasinorm f Hp of a distribution f of H is defined to be the L norm of MΦf (this depends on the choice of Φ, but different choices of Schwartz functions Φ give equivalent norms). The H -quasinorm is a norm when p ≥ 1, but not … WebOct 13, 2012 · Also, we prove that the commutators generated by the p-adic Hardy operators (Hardy-Littlewood-Pólya operators) and the central BMO functions are bounded on L q ( x dx), more generally, on Herz spaces. ... Kim, Y. C.: Carleson measures and the BMO space on the p-adic vector space. Math. Nachr., 282(9), 1278–1304 (2009)
Hardy bmo space
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WebJan 18, 2024 · In this paper we establish the product Hardy spaces associated with the Bessel Schrödinger operator introduced by Muckenhoupt and Stein, and provide … Web(iv) The non-commutative Hardy-Littlewood maximal inequality. (v) A description of BMO as an intersection of two dyadic BMO. (vi) The interpolation results on these Hardy spaces. 0Key words Hardy space, BMO space, Hardy-Littlewood maximal function, von Neumann algebra, non-commutative L p space, interpolation, Lusin integral.
WebAbstract. In this survey we discuss the connection between commutator operators and functions of bounded mean oscillation, and at the same time outline the parallel story of the real Hardy space and weak factorization of these functions. We provide motivation as to why these questions are interesting and highlight the many different methods of ... WebH ·H := h = fg : f, g ∈ H = H ←↩ H is the product space of H2, by inner/outer factorization and Cauchy-Schwarz inequality. It is interesting, then, to find the dual space of H1. C. Fefferman [7] proved that, under the H2 paring (with some care), (H2 ·H2)∗ = (H1)∗ = BMO∩H(D) is the space of the analytic functions with bounded mean oscillation. The …
WebJul 1, 2024 · BMOA-space. In 1961, F. John and L. Nirenberg [a4] introduced the space of functions of bounded mean oscillation, $\operatorname {BMO}$, in their study of … WebThe dual of H 1 is the space BMO of functions of bounded mean oscillation. The space BMO contains unbounded functions (proving again that H 1 is not closed in L 1). If p < 1 then the Hardy space H p has elements that are not functions, and its dual [clarification needed] is the homogeneous Lipschitz space of order n(1/p − 1).
WebFunction on the Space BMO Wenhao Zhang This Open Access Senior Thesis is brought to you by Scholarship@Claremont. It has been accepted for inclusion in this collection by an authorized ... The space BMO 3 1.2. The Hardy-Littlewood Maximal Operator and the Strong Maximal Operator 4 1.3. Overview of the Thesis 5 1.4. Acknowledgement 6 …
WebAbstract. BMO , the space of functions of bounded mean oscillation, was first introduced by F. John and L. Nirenberg in 1961. It became a focus of attention when C. Fefferman proved that BMO is the dual of the (real) Hardy space H 1 in 1971. In the past 30 years, this space was studied extensively by many mathematicians. unleash space uoaWebWe define the real Hardy space Hp as the set of all functions for which the equivalent conditions of the Theorem hold. If p > 1 then any maximal function of f majorizes a multiple of f. The second and the third are bounded by the standard Hardy-Littlewood maximal function and hence Hp = Lp in that case. For p = 1 the same argument shows that ... recetas sin harinaWebThe introduction and development of Hardy and BMO spaces on Euclidean spaces in the 1960s and 1970s played an important role in modern harmonic analysis and applications … unleash speakers