**Proceedings of Symposia in Pure Mathematics**

Volume: 35;
1979;
460 pp;
Softcover

MSC: Primary 42;
Secondary 43

Print ISBN: 978-0-8218-1436-9

Product Code: PSPUM/35.1

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-0-8218-9323-4
Product Code: PSPUM/35.1.E**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

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# Harmonic Analysis in Euclidean Spaces, Part 1

Share this page *Edited by *
*Guido Weiss; Stephen Wainger*

# Table of Contents

## Harmonic Analysis in Euclidean Spaces, Part 1

- Contents of Part I xix20
- Volume contents v6 free
- Photograph of Rivière vi7 free
- Nestor M. Riviere (1940—1978) vii8 free
- Bibliography of N. M. Rivière xv16 free
- Some open questions xvii18 free
- Photographs of participants xxiii24 free
- Preface xxv26 free
- Chapter 1. Real harmonic analysis 128 free
- Some problems in harmonic analysis 330
- On operators of harmonic analysis which are not convolutions 2148
- Maximal functions, covering lemmas and Fourier multipliers 2956
- Covering lemmas, maximal functions and multiplier operators in Fourier analysis 5178
- Besicovitch theory of linearly measurable sets and Fourier analysis 6188
- Weighted norm inequalities for classical operators 6996
- Applications of Fourier transforms to averages over lower dimensional sets 85112
- Hilbert transforms and maximal functions related to variable curves 95122
- Regularity of spherical means 99126
- Restriction theorems for the Fourier transforms to some manifolds in R[sup(n)] 101128
- Restriction theorems for the Fourier transform 111138
- Riesz potentials and Fourier multipliers 115142
- Fourier multipliers vanishing at infinity 121148
- Weighted norm inequalities for the littlewood-Paley function g[sup(*)][sub(λ)] 125152
- Weighted norm inequalities for multipliers 133160
- Non-equivalence between two kinds of conditions on weight functions 141168
- Some remarks about Beckner's inequality 149176
- Hypercontractive estimates for semigroups 159186
- Singular integrals near L[sup(1)] 163190
- On Carleson's convergence theorem for L[sup(2)] functions 167194
- Multiple Fourier series of functions of generalized bounded variation 171198
- Some inequalities for Riesz potentials of trigonometric polynomials of several variables 175202
- A note on Sobolev spaces 183210

- Chapter 2. Hardy spaces and BMO 187214
- Some problems in the theory of Hardy spaces 189216
- Weak-type inequalities for H[sup(P)] and BMO 201228
- Singular integral characterizations of nonisotropic H[sup(P)] spaces and the F. and M. Riesz theorem 231258
- A maximal theory for generalized Hardy spaces 235262
- Local Hardy spaces 245272
- Distributions with strong maximal functions L[sup(p)](R[sup(n)]) 249276
- Weighted Hardy spaces 253280
- Weighted Hardy spaces on lipschitz domains 263290
- The atomic decomposition of Hardy spaces 275302
- The molecular characterization of Hardy spaces 281308
- A characterization of H[sup(1)](∑[sub(n-1)]) 289316
- Two constructions in BMO 295322
- Invariant subspaces and subnormal operators 303330

- Chapter 3. Harmonic functions, potential theory and theory of functions of one complex variable 311338
- Harmonic functions in Lipschitz domains 313340
- A survey of harmonic functions on symmetric spaces 323350
- Positive harmonic functions vanishing on the boundary of certain domains in R[sup(n+1)] 345372
- Positive harmonic functions with zero boundary values 349376
- Harmonic functions with BMO boundary values 353380
- L[sup(P)]-capacitary integrals with some applications 359386
- Sobolev spaces, the Navier-Stokes equations and capacity 369396
- Approximation in L[sup(P)] by analytic and harmonic functions 377404
- On the Helson-Szego theorem and a related class of modified Toeplitz kernels 383410
- Some sharp inequalities for conjugate functions 409436
- Constructions for BMO(R) and A[sub(p)](R[sup(n)]) 417444
- Structure of some subalgebra of L[sup(∞)] of the torus 421448
- A geometric conditions which implies BMOA 427454
- Proof of the Beurling-Malliavin theorem by duality and harmonic estimation 431458
- Zero sets of absolutely convergent Taylor series 439466
- Capacity and uniform algebras 445472
- Following functions of class H[sup(2)] 451478
- A Hankel type operator arising in deformation theory 457484
- Representation theorems for holomorphic and harmonic functions 459486