$R$ -Boundedness versus $\gamma$ -boundedness
نویسندگان
چکیده
منابع مشابه
R-boundedness of Smooth Operator-valued Functions
In this paper we study R-boundedness of operator families T ⊂ B(X, Y ), where X and Y are Banach spaces. Under cotype and type assumptions on X and Y we give sufficient conditions for R-boundedness. In the first part we show that certain integral operator are R-bounded. This will be used to obtain R-boundedness in the case that T is the range of an operator-valued function T : Rd → B(X, Y ) whi...
متن کاملBoundedness versus Periodicity over Commutative Local Rings
Over commutative graded local artinian rings, examples are constructed of periodic modules of arbitrary minimal period and modules with bounded Betti numbers, which are not eventually periodic. They provide counterexamples to a conjecture of D. Eisenbud, that every module with bounded Betti numbers over a commutative local ring is eventually periodic of period 2 . It is proved however, that the...
متن کاملOn R-boundedness of unions of sets of operators
It is shown that the union of a sequence T1, T2, . . . of R-bounded sets of operators from X into Y with R-bounds τ1, τ2, . . ., respectively, is Rbounded if X is a Banach space of cotype q, Y a Banach space of type p, and ∑ ∞ k=1 τ r k <∞, where r = pq/(q−p) if q <∞ and r = p if q =∞. Here 1 ≤ p ≤ 2 ≤ q ≤ ∞ and p 6= q. The power r is sharp. Each Banach space that contains an isomorphic copy of...
متن کاملboundedness of maximal averages over hypersurfaces in R 3
Our goal is to determine for which p is the maximal operator M bounded on L. Note that by subadditivity of maximal operators of the form (1.1), one can prove L boundedness of the nonlocalized analogue of (1.1) over a compact surface by doing a partition of unity and reducing to (1.1). If L is an invertible linear transformation and ML denotes the maximal operator corresponding to the surface L(...
متن کاملOn Rado's Boundedness Conjecture
We prove that Rado’s Boundedness Conjecture from Richard Rado’s 1933 famous dissertation Studien zur Kombinatorik is true if it is true for homogeneous equations. We then prove the first nontrivial case of Rado’s Boundedness Conjecture: if a1, a2, and a3 are integers, and if for every 24-coloring of the positive integers (or even the nonzero rational numbers) there is a monochromatic solution t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2016
ISSN: 0004-2080
DOI: 10.1007/s11512-015-0223-1