Mathematical Sciences: Solvability and Estimates for the    Tangential Cauchy-Riemann Operators
{'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 will be done on the solvability and estimates                      for the tangential Cauchy-Riemann operators.  The global                        problem is an extension of earlier work on square-                              integrable existence and estimates for the boundary d-                          bar operator on weakly pseudo-convex boundaries. Efforts                        to obtain optimal Holder and power integral estimates,                          as well as the nonisotropic properties of the solutions                         will be done.  The method proposed is to construct the                          integral kernels for the operator by fusing the boundary                        invariants and finite type conditions into the                                  construction.  Local solvability under condition Y(q)                           will also be studied using kernel methods.  To obtain                           estimates for the local solution, work is planned on the                        analysis of singular integrals with singularities                               supported on a large set.  Applications to problems of                          prescribing zeros of functions in the Nevanlinna class                          will be pursued.  The generalized Blaschke condition                            must be satisfied on strongly pseudoconvex domains.  The                        solution to this follows lines similar to the planned                           research on weakly pseudo-convex domains.  Some related                         condition may provide the desired classification.
{'FirstName': 'Mei-Chi', 'LastName': 'Shaw', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Mei-Chi Shaw', 'EmailAddress': 'shaw.1@nd.edu', 'NSF_ID': '000195026', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Houston', 'CityName': 'HOUSTON', 'ZipCode': '772043067', 'PhoneNumber': '7137435773', 'StreetAddress': '4300 MARTIN LUTHER KING BLVD', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Texas', 'StateCode': 'TX', 'CONGRESSDISTRICT': '18', 'CONGRESS_DISTRICT_ORG': 'TX18', 'ORG_UEI_NUM': 'QKWEF8XLMTT3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF HOUSTON SYSTEM', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
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