scholarly journals Commutators in real interpolation with quasi-power parameters

2002 ◽  
Vol 7 (5) ◽  
pp. 239-257 ◽  
Author(s):  
Ming Fan
Keyword(s):  
Function Spaces ◽  
Higher Order ◽  
Real Interpolation ◽  
Hardy Inequalities ◽  
Commutator Estimates ◽  
The Real ◽  
Interpolation Methods ◽  
Commutator Theorem

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the real interpolation methods.

Weighted Hardy inequalities, real interpolation methods and vector measures

2014 ◽  
Vol 109 (2) ◽  
pp. 337-352
Author(s):  
Ricardo del Campo ◽  
Antonio Fernández ◽  
Antonio Manzano ◽  
Fernando Mayoral ◽  
Francisco Naranjo
Keyword(s):  
Real Interpolation ◽  
Hardy Inequalities ◽  
Vector Measures ◽  
Interpolation Methods

Some reiteration results for interpolation methods defined by means of polygons

2008 ◽  
Vol 138 (6) ◽  
pp. 1179-1195 ◽  
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera ◽  
Joaquim Martín
Keyword(s):  
Banach Algebras ◽  
Function Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
The Real ◽  
Interpolation Methods ◽  
Real Method

We continue the research on reiteration results between interpolation methods associated to polygons and the real method. Applications are given to N-tuples of function spaces, of spaces of bounded linear operators and Banach algebras.

scholarly journals Stein interpolation for the real interpolation method

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Nick Lindemulder ◽  
Emiel Lorist
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
Complex Interpolation ◽  
The Real ◽  
Interpolation Methods ◽  
Complex Formulation ◽  
Closed Operators ◽  
Real Interpolation Method

AbstractWe prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $$L^p$$ L p -spaces and the sectoriality of closed operators with the real interpolation method.

scholarly journals K-ENVELOPES FOR REAL INTERPOLATION METHODS

2012 ◽  
Vol 55 (2) ◽  
pp. 293-307
Author(s):  
MING FAN
Keyword(s):  
Function Space ◽  
Upper Bounds ◽  
Function Spaces ◽  
Real Interpolation ◽  
Rearrangement Invariant Space ◽  
Interpolation Spaces ◽  
Invariant Space ◽  
Bounded Operators ◽  
Fundamental Function ◽  
Interpolation Methods

AbstractIn this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the KΦ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.

scholarly journals EFEKTIVITAS PEMBELAJARAN BENTUK MOLEKUL DENGAN PEMODELAN REAL BERBASIS PENEMUAN TERBIMBING UNTUK MELATIHKAN KETERAMPILAN BERPIKIR TINGKAT TINGGI SISWA

2017 ◽  
Vol 3 (2) ◽  
pp. 332
Author(s):  
Sutrisno Sutrisno ◽  
Sri Poedjiastoeti ◽  
I Gusti Made Sanjaya
Keyword(s):  
Higher Order Thinking ◽  
Thinking Skills ◽  
Higher Order ◽  
Lesson Plans ◽  
Average Score ◽  
Learning Materials ◽  
Guided Discovery ◽  
Gain Score ◽  
The Real ◽  
Learning And Teaching

This study aimed to describe the effectiveness of learning materials on shape of the molecule with the real modeling supported by PhET media-based on guided discovery to facilitate the students’ high-order-thinking skills at odd semester XI class of SMAN 10. This research is developmental research using 4D models. Thetest of the learning materials use one group pretest-posttest design. The results of validity syllabus (3.87), lesson plans (3.71), students’ book (3.35), work sheet (3.63), and test of products (3.58) are categorized very good and reliability syllabus (99%), lesson plans (100%), students’ book (89%), work sheet (100%), and test of products (100%) are categorized reliable. The Achievement test of higher-order thinking skills showed that the individuals completeness an average score of 82.79, the average sensitivity of items was 0.74 and the average individual gain score of 0.82. Students' response to the learning and teaching activities in average were well-categorized. Based on the findings of the study, it can be concluded that the shape of molecule with the real modeling supported by PhET media based on guided discovery–was effective to train the students' higher-order thinking skills.Penelitian ini bertujuan untukmendeskripsikan efektivitas perangkat pembelajaran bentuk molekul dengan pemodelan real ditunjang media PhET berbasis penemuan terbimbinguntuk melatihkan keterampilan berpikir tingkat tinggi siswa kelas XI semester ganjil SMAN 10 Samarinda pada materi bentuk molekul.Perangkat pembelajaran yang digunakan dikembangkan dengan model 4D. Perangkatpembelajaran di uji cobakan menggunakan one group pretest-posttest design. Validitas Silabus (3,87), RPP (3,71), BAS (3,35), LKS (3,63), dan LP Produk (3,58) berkategori sangat baik dan reliabilitas Silabus (99%), RPP (100%), BAS (89), LKS (100%), LP Produk (100%) berkategori reliabel. Tes hasil belajar keterampilan berpikir tingkat tinggi menunjukkan ketuntasan individual rata-rata 82,79, sensitivitas butir soal rata-rata 0,74 dan gain score individual rata-rata 0,82. Respon siswa terhadap perangkat pembelajaran dan kegiatan pembelajaran rata-rata baik.Berdasarkan temuan hasil penelitian dapat disimpulkan bahwa perangkat pembelajaran bentuk molekul dengan pemodelan real ditunjang media PhET berbasis model penemuan terbimbingefektif untuk melatihkan keterampilan berpikir tingkat tinggi siswa.

scholarly journals Impact on Stability by the Use of Memory in Traub-Type Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 274
Author(s):  
Francisco I. Chicharro ◽  
Alicia Cordero ◽  
Neus Garrido ◽  
Juan R. Torregrosa
Keyword(s):  
Order Of Convergence ◽  
Nonlinear Problems ◽  
Higher Order ◽  
Lower Number ◽  
Dynamical Analysis ◽  
The Real ◽  
Original Scheme ◽  
Interpolation Polynomials ◽  
With Memory ◽  
Number Of Iterations

In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub’s scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process.

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