SHOP.AGUARDIENTECLOTHING.COM Books > Functional Analysis > Integral Operators in Non-Standard Function Spaces: Volume by Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro,

Integral Operators in Non-Standard Function Spaces: Volume by Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro,

By Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

This publication, the results of the authors' lengthy and fruitful collaboration, specializes in essential operators in new, non-standard functionality areas and offers a scientific examine of the boundedness and compactness houses of uncomplicated, harmonic research essential operators within the following functionality areas, between others: variable exponent Lebesgue and amalgam areas, variable Hölder areas, variable exponent Campanato, Morrey and Herz areas, Iwaniec-Sbordone (grand Lebesgue) areas, grand variable exponent Lebesgue areas unifying the 2 areas pointed out above, grand Morrey areas, generalized grand Morrey areas, and weighted analogues of a few of them.

The effects acquired are largely utilized to non-linear PDEs, singular integrals and PDO thought. one of many book's such a lot particular beneficial properties is that most of the statements proved listed here are within the type of criteria.

The publication is meant for a large viewers, starting from researchers within the zone to specialists in utilized arithmetic and potential students.

Show description

Read Online or Download Integral Operators in Non-Standard Function Spaces: Volume 1: Variable Exponent Lebesgue and Amalgam Spaces PDF

Similar functional analysis books

A panorama of harmonic analysis

Tracing a direction from the earliest beginnings of Fourier sequence via to the newest study A landscape of Harmonic research discusses Fourier sequence of 1 and several other variables, the Fourier rework, round harmonics, fractional integrals, and singular integrals on Euclidean area. The climax is a attention of principles from the perspective of areas of homogeneous kind, which culminates in a dialogue of wavelets.

Real and Functional Analysis

This e-book introduces most crucial points of recent research: the speculation of degree and integration and the speculation of Banach and Hilbert areas. it truly is designed to function a textual content for first-year graduate scholars who're already accustomed to a few research as given in a booklet just like Apostol's Mathematical research.

Lineare Funktionalanalysis: Eine anwendungsorientierte Einführung

Die lineare Funktionalanalysis ist ein Teilgebiet der Mathematik, das Algebra mit Topologie und research verbindet. Das Buch führt in das Fachgebiet ein, dabei bezieht es sich auf Anwendungen in Mathematik und Physik. Neben den vollständigen Beweisen aller mathematischen Sätze enthält der Band zahlreiche Aufgaben, meist mit Lösungen.

Additional resources for Integral Operators in Non-Standard Function Spaces: Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

Sample text

Therefore, ˆ ˆ Ip (M w f ) c + c |f (y)|p1 (y)·p− dy = c + c |f (y)|p(y) dy Ω Ω which completes the proof in this case. n M (w) < p (x : reduction to the case of power weights. 39), we may split integration over Ω into two parts, one over a small neighbourhood B(x0 , δ) of the point x0 , and another over its exterior Ω\B(x0 , δ), and to choose δ sufficiently small so that the 0 ,δ))−1 0 )−1 1 number p− (B(x is arbitrarily close to p(x p(x0 ) p(x0 ) = p (x0 ) . 42) =: M1w + M2w + M3w + M4w . Since the weight is strictly positive and bounded beyond any neighbourhood of the point x0 , we get M4w f (x) CM f (x).

13. 37). Then 1 Lr(·) (Rn ) e ς 0 Ap . 2. Convolution Operators 13 Proof. 11) for every m > 0 there holds the (e + |x|)−m with γ e−mAp . Taking m > n and λ = emAp we estimate γ r(x) then have ˆ ˆ r(x) 1 dx dx =: Cm . 39). en−m (m−1)(m−2)···(m−n) . 3 Estimation of the Norm of Convolution Operators ˆ Let k(x − y)f (y) dy Kf (x) := Rn be a convolution operator. 14 are defined by 1 1 1 + , =1− r0 p(∞) q(∞) 1 1 1 =1− + , s0 p− q+ 1 and s0 r0 1 used in s0 . 14. Let p, q ∈ P∞ (Rn ) and q(∞) . p(∞). 38), and 2 case p− = p∞ .

24. Let Ω ⊂ Rn be a bounded open set and p ∈ Plog (Ω). 28), if n r p(xk ) wk (r) ∈ Φ0n , k = 1, 2, . . , N, or, equivalently, if the MO indices of the functions wk (r) satisfy the conditions − n < m(wk ) p(xk ) M (wk ) < Proof. We have to show that M w f equivalent to Ip (M w f ) c for f n , k = 1, 2, . . , N. p (xk ) c in some ball f p(·) Ip (M f ) p(·) f (y) w(|y − x0 |) w(|x − x0 |)p(x0 ) M c Ω We first prove the bound M w f − where 1 q0 = p− −1 p(x0 ) . p(·) n < m(w) p(x0 ) Observe that 1 q0 R, which is p(·) R.

Download PDF sample

Rated 4.44 of 5 – based on 19 votes