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Integral Operators in Non-Standard Function Spaces

Part of the Operator Theory: Advances and Applications Book Series (volume 248)

DOI: 10.1007/978-3-319-21015-5

ISBN: 978-3-319-21014-8

Publisher: Springer International Publishing - Springer Journals

May 12, 2016

1 - 10 of 10 Chapters

LitStream

Chapter 1Hardy-type Operators in Variable Exponent Lebesgue Spaces

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

Pages: 1 –26

[In this chapter we consider the Hardy-type operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 2Maximal, Singular, and Potential Operators in Variable Exponent Lebesgue Spaces with Oscillating Weights

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

Pages: 27 –128

[In this chapter we present estimations for maximal, singular, and potential operators in variable exponent Lebesgue spaces with oscillating weights.]
LitStream

Chapter 3Kernel Integral Operators

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

Pages: 129 –217

[This chapter is devoted mainly to the study of the boundedness/compactness of the weighted Volterra integral operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
LitStream

Chapter 4Two-weight Estimates

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

Pages: 219 –295

[In this chapter two-weight boundedness problems for various integral operators in variable exponent Lebesgue spaces defined on Euclidean, as well as quasimetric measure spaces are explored.]
LitStream

Chapter 5One-sided Operators

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

Pages: 297 –354

[This chapter is devoted to the study of the behavior of one-sided maximal functions, Calderón–Zygmund integrals, and potentials in Lp(.)(I) spaces, where I is an interval of ℝ.]
LitStream

Chapter 6Two-weight Inequalities for Fractional Maximal Functions

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

Pages: 355 –394

[In this chapter necessary and sufficient conditions for boundedness of the fractional maximal functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...
LitStream

Chapter 7Description of the Range of Potentials, and Hypersingular Integrals

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

Pages: 395 –438

[In this chapter we give a complete characterization of the range Iα[Lp(.)(ℝn)] in terms of the convergence of hypersingular integrals of order α. The proof is based, in particular, on the results on denseness in Lp(.)(ℝn) of Schwartz functions orthogonal to polynomials, and the inversion of the...
LitStream

Chapter 8More on Hypersingular Integrals and Embeddings into Hölder Spaces

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

Pages: 439 –454

[In this chapter we present results on hypersingular operators of order α < 1 acting on some Sobolev type variable exponent spaces, where the underlying space is a quasimetric measure space. The proofs are based on some pointwise estimations of differences of Sobolev functions. These estimates...
LitStream

Chapter 9More on Compactness

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

Pages: 455 –465

[In this chapter we present in Section 9.1 two general compactness results convenient for applications. One is the so-called dominated compactness theorem for integral operators. We give it in a general context of Banach Function Spaces (BFS) in the well-known sense (see Bennett and Sharpley...
LitStream

Chapter 10Applications to Singular Integral Equations

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

Pages: 467 –528

[We give an application of the weighted results obtained in Theorem 2.45 with power weights to the theory of Fredholm solvability of singular integral equations (10.1) with piecewise continuous coefficients. As is well known to researches in this field, to investigate such equations in a specific...

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