Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / / Gerald B. Folland, Elias M. Stein.
The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal f...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2022] ©1982 |
Year of Publication: | 2022 |
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Folland, Gerald B., author. aut http://id.loc.gov/vocabulary/relators/aut Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / Gerald B. Folland, Elias M. Stein. Princeton, NJ : Princeton University Press, [2022] ©1982 1 online resource (286 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Notes ; 28 Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Remarks on Notation -- CHAPTER 1 Background on Homogeneous Groups -- CHAPTER 2 Maximal Functions and Atoms -- CHAPTER 3 Decomposition and Interpolation Theorems -- CHAPTER 4 Other Maximal Function Characterizations of HP -- CHAPTER 5 Duals of HP spaces: Campanato Spaces -- CHAPTER 6 Convolution Operators on HP -- CHAPTER 7 Characterization of HP by Square Functions: The Lusin and Littlewood-Paley Functions -- CHAPTER 8 Boundary Value Problems -- BIBLIOGRAPHY -- Index of Terminology -- Index of Notation restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group.The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Jun 2022) Functions of real variables. Hardy spaces. Lie groups. MATHEMATICS / Complex Analysis. bisacsh "admissible. Campanato space. Campbell-Hausdorff formul. Chebyshev's inequality. Constants. Derivatives and multiindices. Dilations. Hardy space. Hardy-Littlewood maximal function. Heisenberg group. Littlewood-Paley function. Lusin function. Maximal functions. Norms. Other operations on functions". Poisson kernel. Poisson-Szegö kernel. area integral. associated (to a ball). atom. atomic Hardy space. atomic decomposition. ball. commutative approximate identity. convolution. dilations. distribution function. graded. grand maximal function. heat kernel. heat semigroup. isotropic degree. kernel of type. lower central series. nilpotent. nonincreasing rearrangement. nontangential maximal function. p-admissible. polynomial. polyradial. positive operator. quasinorms. seminorms. Stein, Elias M., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 9783110494921 ZDB-23-PMN Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Gap Years 9783110784237 https://doi.org/10.1515/9780691222455?locatt=mode:legacy https://www.degruyter.com/isbn/9780691222455 Cover https://www.degruyter.com/document/cover/isbn/9780691222455/original |
language |
English |
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eBook |
author |
Folland, Gerald B., Folland, Gerald B., Stein, Elias M., |
spellingShingle |
Folland, Gerald B., Folland, Gerald B., Stein, Elias M., Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / Mathematical Notes ; Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Remarks on Notation -- CHAPTER 1 Background on Homogeneous Groups -- CHAPTER 2 Maximal Functions and Atoms -- CHAPTER 3 Decomposition and Interpolation Theorems -- CHAPTER 4 Other Maximal Function Characterizations of HP -- CHAPTER 5 Duals of HP spaces: Campanato Spaces -- CHAPTER 6 Convolution Operators on HP -- CHAPTER 7 Characterization of HP by Square Functions: The Lusin and Littlewood-Paley Functions -- CHAPTER 8 Boundary Value Problems -- BIBLIOGRAPHY -- Index of Terminology -- Index of Notation |
author_facet |
Folland, Gerald B., Folland, Gerald B., Stein, Elias M., Stein, Elias M., Stein, Elias M., |
author_variant |
g b f gb gbf g b f gb gbf e m s em ems |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Stein, Elias M., Stein, Elias M., |
author2_variant |
e m s em ems |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Folland, Gerald B., |
title |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / |
title_full |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / Gerald B. Folland, Elias M. Stein. |
title_fullStr |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / Gerald B. Folland, Elias M. Stein. |
title_full_unstemmed |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / Gerald B. Folland, Elias M. Stein. |
title_auth |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / |
title_alt |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Remarks on Notation -- CHAPTER 1 Background on Homogeneous Groups -- CHAPTER 2 Maximal Functions and Atoms -- CHAPTER 3 Decomposition and Interpolation Theorems -- CHAPTER 4 Other Maximal Function Characterizations of HP -- CHAPTER 5 Duals of HP spaces: Campanato Spaces -- CHAPTER 6 Convolution Operators on HP -- CHAPTER 7 Characterization of HP by Square Functions: The Lusin and Littlewood-Paley Functions -- CHAPTER 8 Boundary Value Problems -- BIBLIOGRAPHY -- Index of Terminology -- Index of Notation |
title_new |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / |
title_sort |
hardy spaces on homogeneous groups. (mn-28), volume 28 / |
series |
Mathematical Notes ; |
series2 |
Mathematical Notes ; |
publisher |
Princeton University Press, |
publishDate |
2022 |
physical |
1 online resource (286 p.) |
contents |
Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- Remarks on Notation -- CHAPTER 1 Background on Homogeneous Groups -- CHAPTER 2 Maximal Functions and Atoms -- CHAPTER 3 Decomposition and Interpolation Theorems -- CHAPTER 4 Other Maximal Function Characterizations of HP -- CHAPTER 5 Duals of HP spaces: Campanato Spaces -- CHAPTER 6 Convolution Operators on HP -- CHAPTER 7 Characterization of HP by Square Functions: The Lusin and Littlewood-Paley Functions -- CHAPTER 8 Boundary Value Problems -- BIBLIOGRAPHY -- Index of Terminology -- Index of Notation |
isbn |
9780691222455 9783110494921 9783110442496 9783110784237 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA331 |
callnumber-sort |
QA 3331.5 F64 41982EB |
url |
https://doi.org/10.1515/9780691222455?locatt=mode:legacy https://www.degruyter.com/isbn/9780691222455 https://www.degruyter.com/document/cover/isbn/9780691222455/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.7/3 |
dewey-sort |
3515.7 13 |
dewey-raw |
515.7/3 |
dewey-search |
515.7/3 |
doi_str_mv |
10.1515/9780691222455?locatt=mode:legacy |
oclc_num |
1312726252 |
work_keys_str_mv |
AT follandgeraldb hardyspacesonhomogeneousgroupsmn28volume28 AT steineliasm hardyspacesonhomogeneousgroupsmn28volume28 |
status_str |
n |
ids_txt_mv |
(DE-B1597)573089 (OCoLC)1312726252 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Gap Years |
is_hierarchy_title |
Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 / |
container_title |
Title is part of eBook package: De Gruyter Princeton Mathematical Notes eBook-Package 1970-2016 |
author2_original_writing_str_mv |
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