2 edition of **Weighted norm inequalities for integral transforms with product kernals** found in the catalog.

Weighted norm inequalities for integral transforms with product kernals

V. M. Kokilashvili

- 78 Want to read
- 34 Currently reading

Published
**2009**
by Nova Science Publishers in Hauppauge, NY
.

Written in English

- Inequalities (Mathematics),
- Integral transforms

**Edition Notes**

Includes bibliographical references and index.

Statement | Vakhtang Kokilashvili , Alexander Meskhi, and Lars-Erik Persson. |

Contributions | Meskhi, Alexander., Persson, Lars Erik, 1944- |

Classifications | |
---|---|

LC Classifications | QA295 .K755 2009 |

The Physical Object | |

Pagination | p. cm. |

ID Numbers | |

Open Library | OL23397319M |

ISBN 10 | 9781607415916 |

LC Control Number | 2009021063 |

WEIGHTED NORM INEQUALITIES FOR MAXIMALLY MODULATED SINGULAR INTEGRAL OPERATORS LOUKAS GRAFAKOS, JOSE MAR´ ´IA MARTELL, AND FERNANDO SORIA Weighted inequalities, vector-valued estimates, modulated singular integrals, This deﬁnition is motivated by the Carleson operator in which T is the Hilbert transformCited by: Wheeden R.L. () Weighted Norm Estimates for Singular Integrals with LlogL Kernels: Regularity of Weak Solutions of Some Degenerate Quasilinear Equations. In: Georgakis C., Stokolos A., Urbina W. (eds) Special Functions, Partial Differential Equations, and Harmonic : Richard L. Wheeden.

One goal of this paper is to show that a big number of inequalities for functions in \(L^{p}(R_{+})\), \(p\geq1\), proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp new results are also included, e.g. the similar general Cited by: 1. Grafakos L, Liu L, Yang D. Multiple-weighted norm inequalities for maximal multilinear singular integrals with non-smooth kernels. Proc Roy Soc Edinburgh Sect A, , – zbMATH MathSciNet CrossRef Google ScholarCited by: 1.

Weighted Norm Inequalities for the Local Sharp Maximal Function Corollary 1. Inequalities () and () are sharp in the sense that M[p]+1ω cannot be replaced by M[p]ω. To prove Proposition 1, we follow a counterexample due to J.M. Wilson [16]. Let n = 1 and T be the Hilbert transform H. Take ω = χ(0,1) and f = (logx)−1χ (e,eN). Convexity, Inequalities, and Norms 9 Applying the same reasoning using the integral version of Jensen’s inequality gives p q) Z X fpd 1=p X fqd 1=q for any L1 function f: X!(0;1), where (X;) is a measure space with a total measure of one. Norms A norm is a function that measures the lengths of vectors in a vector space. TheFile Size: KB.

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The book may be considered as a systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. The considered product kernels cover that case when factors of kernels Cited by: The book may be considered as a systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view.

The considered product kernels cover that case when factors of kernels have essential (less than one). ISBN: OCLC Number: Description: xiii, pages: illustrations ; 26 cm.

Contents: Preface; Hardy & Polya-Knopp Inequalities; Weighted Boundedness Criteria for Integral Transforms with Product Kernels; One-Sided Fractional Multiple Operators; Strong Fractional Maximal Functions & Multiple Riesz Potentials; Strong Maximal Functions & Hilbert Transforms.

Our second result is the weighted norm inequalities for these operators T 1 T 2, T 1 ∘ T 2 and fractional differentiation operators D γ for 0 Theorem Let 0, 1 Cited by: 2. Weighted norm inequality for the singular integral with variable kernel and fractional differentiation Article in Journal of Mathematical Analysis and Applications (2) October with 25 Reads.

Abstract. The aim of this paper is to establish a sufficient condition for certain weighted norm inequalities for singular integral operators with non-smooth kernels and for the commutators of these singular integrals with BMO functions. Our condition is applicable to various singular integral operators, such as the second derivatives Cited by: 4.

The unifying thread of this book is the topic of Weighted Norm Inequalities, but many other related topics are covered, including Hardy spaces, singular integrals, maximal operators, functions of bounded mean oscillation and vector valued inequalities. For bounded Lebesgue measurable functionsα,βon the unit circle,Sα,β=αP++βP−is called a singular integral operator, whereP+is an analytic projection an Cited by: 3.

Weighted Sobolev space on half line. Let for. For a positive continuous weight on, we denote { ∫ } a weighted Sobolev space of functions, real-valued and absolutely continuous on, with the norm () (∫) In the case of, this space is denoted by.

Let us consider the nonlinear transform () by: problem when there are different weight functions on the two sides of the inequality, the case whenp = l orp = oo, a weighted definition of the maximal function, and the result in higher dimensions.

Applications of the results to mean summability of Fourier and. NORM INEQUALITIES FOR FRACTIONAL INTEGRALS 5 When p > 1 this is an immediate consequence of the inequality relating I 1 and the gradient, and the strong type norm inequality for I 1.

When p= 1 it can be proved using the weak type inequality for I 1 and a decomposition argument due to Maz0ya [65, p. ] (see also Long and Nie [64] and [21 File Size: KB. [16] WEIGHTED NORM INEQUALITIES FOR INTEGRAL TRANSFORMS WITH PRODUCT KERNALS (together with Alexander Meshki and Vakhtang Kokalishvili), NOVA SCIENTIFIC PUBLISHERS, INC., NEW YORK, ( pages).

[17] MATHEMATICAL INEQUALITIES AND APPLICATIONS. Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities.

Introduction and. H¨ older’s inequalities we established weighted 𝐿 𝑝, 𝑝 > 1, norm inequalities for these iterated convolutions. In this pap er, by using the reverse H¨ older’s inequalities we will. Weighted norm inequalities with general weights are established for the maximal singular integral operators on spaces of homogeneous type, when the kernel satisfies a Hörmander regularity condition on one variable and a Hölder regularity condition on the other variable.

Previous article in Cited by: 4. Weighted norm inequalities for fractional integrals. Authors: Benjamin Muckenhoupt, and Richard Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A Retrieve articles in all journals.

We study weighted norm inequalities for singular integral operators with diﬀerent smooth- ness conditions assumed on the kernels. The weakest one is the so-called classical H¨ormander condition, which is an L 1 regularity, and the strongest is given by a H¨older or Lipschitz.

Various weighted (L p) (p>1) norm inequalities in convolutions are derived by a simple and general principle whose L 2 version previously was given by the idea of products in Hilbert spaces introduced through their transforms and obtained by using the theory of reproducing kernels.

Weighted norm inequalities appear in many places in analysis, for example, for Hardy-Littlewood maximal functions, singular in-tegrals, pseudo-differential operators, Fourier series etc. In this note we shall investigate weighted norm inequalities for pseudo-differential operators.

Let m(x, ξ) be a sufficiently regular function denned on. We give some new type of convolution inequalities in weighted L p (R 2,dxdy) spaces and their important applications to partial differential equations and integral transforms. Purchase Weighted Norm Inequalities and Related Topics, Volume - 1st Edition.

Print Book & E-Book. ISBNBook Edition: 1.Weighted norm inequalities for singular integral operators C. P´erez Journal of the London mathematical society 49 (), – The purpose of this paper is to prove weighted norm inequalities of the form (2), where M rw, adjoint operator of T.

T∗ is also a singular integral operator with kernel Cited by: Sharp weighted norm inequalities for Littlewood–Paley operators and singular integrals j+1 2 k) for some integers j and k.

dyadic cube Q âŠ‚ R n is a Cartesian product of n dyadic intervals of equal lengths. vol.Springer-Verlag, [25] J.

Wittwer, A sharp estimate on the norm of the martingale transform, Math. Res Cited by: