Mathematical Sciences: Weighted norm inequalities and       applications
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work will continue on weighted norm inequalities for various            classical operators and operators related to orthogonal                         polynomial expansions.  Applications of these inequalities to                   differential equations will also be examined.  The norm                         inequalities to be considered concern fractional integrals,                     Sobolev interpolation inequalities, Fourier transforms, weighted                Hardy and Lebesgue product spaces, n-dimensional Hardy's                        inequality, Littlewood-Paley functions and Hilbert transforms.                  The basic problem in all these situations is that of                            understanding the character of the weight functions for which                   weighted norm inequalities hold.                                                        The operators related to orthogonal polynomial expansions               are Cesaro sum operators and transplantation operators for                      Hermite and Laguerre polynomials.  Weak and strong type norm                    inequalities will be proved by obtaining accurate kernel                        estimates.                                                                              Applications to differential equations concern the                      regularity of solutions of degenerate elliptic equations.  In                   case the degeneracy is governed by two weight functions, the                    problems include estimates of the Green function and norm                       inequalities for the potentials associated with it.  With equal                 weights, the problem is how the weight affects the smoothness of                the solutions when the coefficients are assumed to have some                    smoothness.  A local version of Harnack's inequality will also be               investigated for equations whose coefficients are not smooth and                degenerate differently in different directions.
{'FirstName': 'Richard', 'LastName': 'Wheeden', 'PI_MID_INIT': 'L', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Richard L Wheeden', 'EmailAddress': 'wheeden@math.rutgers.edu', 'NSF_ID': '000228704', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Rutgers University New Brunswick', 'CityName': 'NEW BRUNSWICK', 'ZipCode': '089018559', 'PhoneNumber': '8489320150', 'StreetAddress': '3 RUTGERS PLZ', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'M1LVPE5GLSD9', 'ORG_LGL_BUS_NAME': 'RUTGERS, THE STATE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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