Download Geometry of Banach spaces: Selected topics by J. Diestel PDF

By J. Diestel

ISBN-10: 0387074023

ISBN-13: 9780387074023

ISBN-10: 3540074023

ISBN-13: 9783540074021

Show description

Read or Download Geometry of Banach spaces: Selected topics PDF

Similar functional analysis books

Nonlinear Functional Analysis

This graduate-level textual content deals a survey of the most principles, recommendations, and strategies that represent nonlinear useful research. It good points large observation, many examples, and fascinating, difficult workouts. issues contain measure mappings for countless dimensional areas, the inverse functionality thought, the implicit functionality conception, Newton's equipment, and lots of different topics.

A Basis Theory Primer: Expanded Edition

The classical topic of bases in Banach areas has taken on a brand new lifestyles within the smooth improvement of utilized harmonic research. This textbook is a self-contained creation to the summary concept of bases and redundant body expansions and its use in either utilized and classical harmonic research. The 4 elements of the textual content take the reader from classical sensible research and foundation idea to trendy time-frequency and wavelet idea.

INVERSE STURM-LIOUVILLE PROBLEMS AND THEIR APPLICATIONS

This e-book offers the most effects and techniques on inverse spectral difficulties for Sturm-Liouville differential operators and their functions. Inverse difficulties of spectral research consist in recuperating operators from their spectral features. Such difficulties usually look in arithmetic, mechanics, physics, electronics, geophysics, meteorology and different branches of ordinary sciences.

Extra info for Geometry of Banach spaces: Selected topics

Sample text

1. Let 1 L p,λ f∈ (Ω) = Lploc (Ω) 0. The Morrey space Lp,λ (Ω) is defined as ˆ 1 : sup λ r x∈Ω;r>0 |f (y)|p dy < ∞ . 1) B(x,r) This is a Banach space with respect to the norm f Lp,λ (Ω) := sup x∈Ω;r>0 ˆ 1 rλ 1 p |f (y)| dy p . 2) B(x,r) Note that if we want to have an equivalent norm in the form ˆ 1 sup 1 p |f (y)| dy p λ |B(x, r)| n x∈Ω;r>0 , B(x,r) we should assume that Ω satisfies the condition |B(x, r)| Crn , 0 < r < diam (Ω), which is done, for instance, in the book of Kufner, John, and Fuˇc´ık [151].

54) be satisfied. 49), the operator I α(·) is bounded from the space H ω(·) (Ω) to the weighted space H ωα (·) (Ω, α). Proof. 19. 28. 55) reduces to sup [λ(x) + Re α(x)] < θ. 3. Potentials of Constant Order 593 In the following theorem we use the notation ω−α (x, t) = t− Re α(x) ω(x, t) and ω−α (x, h) = sup ω−α (y, h) y:|y−x|

2]. 18. Let ω(x, t) be in ∈ W (0, ) uniformly in x. Then ω(x, t) ∈ Zβ ⇐⇒ M (w) < β. 17. 19. Let ωδ = ω(x,t) tδ(x) and ωβ = ω(x,t) . 36) ω(x, t) ∈ Zβ(·) ⇐⇒ M (wβ ) < 0. 37) take the form ω(x, t) ∈ Zδ(·) ⇐⇒ ω(x, t) ∈ Zβ(·) ⇐⇒ inf [m(w, x) − δ(x)] > 0, x∈Ω sup[M (w, x) − β(x)] < 0. x∈Ω We will make use of the following property of the bounds for functions ω(x, t) ∈ W(T) in terms of their indices: c1 tM(w)+ε ω(x, t) c2 tm(ω)−ε , 0 t (< ∞), where ε > 0 and the constants c1 , c2 may depend on ε, but do not depend on x and t (see Samko [192, Thm.

Download PDF sample

Rated 4.92 of 5 – based on 30 votes