Mathematical Sciences: Multi-Parameter Harmonic Analysis andLittlewood-Paley Inequalities
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work to be done on this project will focus on problems                     arising in the modern theory of harmonic analysis and its                       relationship with partial differential equations.  This                         relationship arises naturally when differential equations are                   transformed by various means into integral expressions or                       operators.  In 1976, the fundamental inequalities relating                      bounds of Calderon-Zygmund operate to weighted function norms                   were obtained.  Extensive work on these estimates followed, but                 most work was confined to one-parameter operators.  In this                     project, a multiparameter theory is laid out for investigation.                  The basic inequalities are much harder to achieve in this                      context because of the complexities of higher dimentional                       analogues to dyadic intervals.  Nevertheless, inequalities have                 been established for the two parameter case.  Applications are                  to be made to elliptic operators such as two-parameter                          Schrodinger operators and the development of a                                  correspondinguncertainty principle.
{'FirstName': 'James Michael', 'LastName': 'Wilson', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'James Michael Wilson', 'EmailAddress': 'jmwilson@uvm.edu', 'NSF_ID': '000454243', 'StartDate': '02/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Vermont & State Agricultural College', 'CityName': 'BURLINGTON', 'ZipCode': '054051704', 'PhoneNumber': '8026563660', 'StreetAddress': '85 S PROSPECT STREET', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Vermont', 'StateCode': 'VT', 'CONGRESSDISTRICT': '00', 'CONGRESS_DISTRICT_ORG': 'VT00', 'ORG_UEI_NUM': 'Z94KLERAG5V9', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF VERMONT & STATE AGRICULTURAL COLLEGE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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