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2014, Annals of mathematics studies, ISBN 9780691162515, Volume number 189, xiii, 395 pages
This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical... 
Singular integrals | Transformations (Mathematics) | Mathematical Analysis, PBK- PBKL | Mathematics | Calculus, Mathematics | Singular Integrals
Book
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 1, pp. 289 - 308
In this paper we characterize a class of normal (isometric, coisometric, unitary, hyponormal) singular Cauchy integral operators with operator-valued (or... 
Unitary | Hyponormal | Isometry | Self-adjoint | Normal | Singular integral operators | MATHEMATICS | MATHEMATICS, APPLIED | HYPONORMALITY | HANKEL-OPERATORS | BLOCK TOEPLITZ-OPERATORS | SUBNORMALITY
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2019, Volume 25, Issue 4, pp. 2141 - 2149
We establish the boundedness on Lp(Rn) of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase... 
spaces | Oscillatory integrals | Singular integrals | Lp spaces | Primary 42B20 | MATHEMATICS, APPLIED | Secondary 42B35
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2018, Volume 12, Issue 4, pp. 917 - 929
In this paper, we study the singular integral operator induced by the reproducing kernel of the Drury–Arveson space $$\begin{aligned} Kf(z) =\int _{\mathbb... 
Unit ball | Singular integral operator | Reproducing kernel | Operator Theory | 47G10 | Analysis | Drury–Arveson space | 47B34 | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Drury-Arveson space
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 6/2019, Volume 91, Issue 3, pp. 1 - 18
We establish the weak type estimates of singular integral operators on Morrey spaces built on Banach function space. In particular, we have these weak type... 
Morrey spaces | Primary 42B20 | 42B25 | Analysis | Banach function space | 46E30 | Weak type estimates | Mathematics | variable exponent | Secondary 42B35 | Singular integral operators | INEQUALITIES | BOUNDEDNESS | KERNELS | EXTRAPOLATION | MATHEMATICS | BOUNDS | NAVIER-STOKES | WEIGHTS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2016, Volume 441, Issue 2, pp. 529 - 548
In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2↦L2 type for... 
Helmholtz equation | Singular integral | Oscillating surface | Maximal operator | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 05/2012, Volume 231, Issue 14, pp. 4885 - 4903
We describe a modified Nyström method for the discretization of the weakly singular boundary integral operators which arise from the formulation of linear... 
Elliptic boundary value problems | Integral operators | Singular domains | Scattering theory | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | QUADRATURE | NUMERICAL CUBATURES | BEM | PHYSICS, MATHEMATICAL | CURVES | Analysis | Atmospheric physics | Methods
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 01/2017, Volume 290, Issue 1, pp. 75 - 96
A systematic treatment is given of several classes of parametric Marcinkiewicz integrals. The boundedness on Triebel–Lizorkin spaces will be presented for... 
42B25 | 47G10 | 42B20 | Marcinkiewicz integrals | Besov spaces | rough kernel | Triebel–Lizorkin spaces | MATHEMATICS | Triebel-Lizorkin spaces | REVOLUTION | ROUGH KERNELS | BOUNDEDNESS | L-P BOUNDS | SINGULAR-INTEGRALS | SURFACES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 5, pp. 1073 - 1097
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is... 
Singular integrals | Extrapolation | Weighted norm inequalities | Fractional integrals | Sharp bounds | Maximal operators | MATHEMATICS | NORM INEQUALITIES | SPACES
Journal Article
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, ISSN 1069-5869, 12/2017, Volume 23, Issue 6, pp. 1408 - 1425
In this paper we study singular oscillatory integrals with a nonlinear phase function. We prove estimates of and type. 
MATHEMATICS, APPLIED | Nonlinear phase function | Oscillatory integral | Singular integral
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2014, Volume 413, Issue 1, pp. 502 - 524
Representations on Hilbert spaces for a nonlocal C⁎-algebra B of singular integral operators with piecewise slowly oscillating coefficients extended by a group... 
[formula omitted]-algebra | Singular integral operator with shifts | Faithful representation | Fredholmness | Piecewise slowly oscillating function | algebra | MATHEMATICS | MATHEMATICS, APPLIED | SPACES | C-algebra | Algebra
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2016, Volume 444, Issue 1, pp. 230 - 250
In this paper we introduce new conditions on a kernel of a linear Fredholm integral operator which turn out to be sufficient and necessary for that operator to... 
Leray–Schauder degree | ϕ- and Λ-variation | Linear integral operator of a Fredholm-type | Nonlinear Hammerstein integral equation | Variation in the sense of Jordan | Weakly singular kernel | MATHEMATICS | MATHEMATICS, APPLIED | Leray-Schauder degree | phi- and Lambda-variation | Computer science
Journal Article
JOURNAL OF GEOMETRIC ANALYSIS, ISSN 1050-6926, 10/2017, Volume 27, Issue 4, pp. 2725 - 2757
Let E subset of C be a Borel set such that 0 < H-1(E) < infinity. David and Leger proved that the Cauchy kernel 1/z (and even its coordinate parts Re... 
MATHEMATICS | Singular integrals | Rectifiability | ANALYTIC CAPACITY | LIPSCHITZ-CURVES | Calderon-Zygmund kernels | Cytokinins | Mathematics - Classical Analysis and ODEs
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2017, Volume 111, Issue 4, pp. 931 - 946
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 12/2018, Volume 111, Issue 6, pp. 633 - 646
In this article we generalize the singular integral operator theory on weighted tent spaces to spaces of homogeneous type. This generalization of operator... 
Fefferman–Stein box maximal functions | Off-diagonal estimates | Spaces of homogeneous type | Tent spaces | Maximal regularity | Mathematics | Carleson type functionals | 47A60 | 47D06 | 42B35 | 42B20 | Mathematics, general | Pointwise estimates | 42B37 | Singular integral operators | MATHEMATICS | Fefferman-Stein box maximal functions
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2012, Volume 175, Issue 3, pp. 1473 - 1506
For a general Calderón—Zygmund operator T on ℝ N , it is shown that $\normal{||Tf||_{L^{2}(w)} \le C(T) \cdot \underset {Q}\sup} \LARGE{(}... 
Mathematical theorems | Conditional probabilities | Mathematical integrals | Cubes | Dyadics | Mathematical inequalities | Mathematical functions | Preprints | Martingales | MATHEMATICS | INEQUALITIES | AHLFORS-BEURLING OPERATOR | PLANE | LEBESGUE SPACES | SINGULAR-INTEGRALS | TRANSFORMS
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 12/2017, Volume 23, Issue 6, pp. 1408 - 1425
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2017, Volume 316, pp. 255 - 291
The one-dimensional oscillatory integral operator associated to a real analytic phase S is given byTλf(x)=∫−∞∞eiλS(x,y)χ(x,y)f(y)dy. In their fundamental work,... 
Oscillatory integral operator | Resolution of singularities | Newton Polygon | Van der Corput Lemma | PHASES | VAN | RADON TRANSFORMS | STABILITY | RESOLUTION | LEMMA | HARDY-SPACES | MATHEMATICS | VARIABLES | CORPUT | SINGULAR-INTEGRALS
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 1/2015, Volume 176, Issue 1, pp. 1 - 15
This paper is mostly a review paper. It contains a description of old and recent results concerning the regularity conditions on a Jordan curve in the plane... 
Singular integral operator | Boundary value problem | Mathematics, general | Mathematics | Cauchy integral | Primary 30E20 | 30E25 | Secondary 45E05 | MATHEMATICS | RECTIFIABILITY | LIPSCHITZ-CURVES | ANALYTIC CAPACITY
Journal Article
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