The space $H\sp p$ with $0 < p < 1$

THE SPACE Hp WITH 0<p<l

L p-SPACES FOR 0 < p < 1

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

1 Sketch for F p Estimation when 0 < p ≤ 2

We have seen a linear sketching estimate for F2 estimation that uses O(log n) space. Indyk [1] obtained a technically sophisticated and interesting sketch for Fk estimation where 0 < p ≤ 2 (note that p can be a real number) which uses polylog(n) space. Since the details are rather technical we will only give the high-level approach and refer the reader to the paper and related notes for more de...

0 UG - 00 - 20 Spin ( p + 1 , p + 1 ) Covariant D p – brane Bound States

We construct Spin(p+1, p+1) covariant Dp–brane bound states by using that the potentials in the RR sector of toroidically compactified type II supergravity transform as a chiral spinor of the T–duality group. As an application, we show the invariance of the zero–force condition for a probe D–brane under noncommutative deformations of the background, which gives a holographic proof of the stabil...

THE “ FULL MÜNTZ THEOREM ” IN L p [ 0 , 1 ] FOR 0 < p < ∞ Tamás Erdélyi and William

Tamás Erdélyi and William B. Johnson Abstract. Denote by span{f1, f2, . . . } the collection of all finite linear combinations of the functions f1, f2, . . . over R. The principal result of the paper is the following. Theorem (Full Müntz Theorem in Lp(A) for p ∈ (0,∞) and for compact sets A ⊂ [0, 1] with positive lower density at 0). Let A ⊂ [0, 1] be a compact set with positive lower density a...