Raymond L. Johnson

### Personal

 First Name: Raymond
 Middle Name: L.
 Last Name: Johnson

### Education

 College: University Of Texas
 Degree: B.S.
 RESEARCH NOTES Dr. Raymond L. Johnson has 25 publications on mathematics research. SELECTED PUBLICATIONS (with C. J. Neugebauer) Properties of BMO functions whose reciprocals are also BMO, Z. Anal. Anwendungen 12 (1993), 3--11. (with C. J. Neugebauer) Change of variable results for $A\sb p$- and reverse Hölder ${\rm RH}\sb r$-classes, Trans. Amer. Math. Soc. 328(1991), 639--666. (with C. J. Neugebauer) Homeomorphisms preserving $A\sb p$, Rev. Mat. Iberoamericana 3 (1987), 249--273. (with J. J. Benedetto, J. J. and H. P. Heinig) Weighted Hardy spaces and the Laplace transform. II, Math. Nachr. 132 (1987), 29--55. Application of Carleson measures to partial differential equations and Fourier multiplier problems, Harmonic analysis, Lecture Notes in Math. 992 (1983), 16--72. Definition of generalized Carleson measures and applications, Topics in modern harmonic analysis, Vol. I, II (1982), 627--643, Ist. Naz. Alta Mat. Francesco Severi. Multipliers of $H\sp{p}$ spaces, Ark. Mat. 16 (1978), 235--249. Temperatures, Riesz potentials, and the Lipschitz spaces of Herz, Proc. London Math. Soc. 27 (1973), 290--316. A priori estimates and unique continuation theorems for second order parabolic equations, Trans. Amer. Math. Soc. 158 (1971), 167--177. SUMMA Ray Johnson web page: http://www.maa.org/summa/archive/JohnsRy.htm You can get there even from Alice,Texas I would describe my life, including my entry into the profession, as being characterized by my coming of age on the right side of several transition points from the totally segregated society in which I grew up to the quasi-open society in which we now live. I grew up in Alice, Texas where I attended an all-black two room schoolhouse with four grades to a room. There was a new elementary school within stone's throw of my house but it was restricted to whites and Hispanics. I walked six blocks past the new school to attend my two room school. One advantage of the small school was that the teachers knew the students very well. As a result of my grandfather having taught me to read, I was skipped two grades. I had learned some mathematics from him and did well in mathematics as a result. Alice wasn't big enough to have an all-black upper level school; black students were bused 28 miles to Kingsville, Texas for education from grades 9 through 12. Brown vs. Board of Education was decided the year before I was to start ninth grade, and the Alice School Board chose to abide by it. When I entered high school, I was lucky enough to be affected by another transition event in American history. The Russians launched Sputnik. There was lots of effort put into improving science education in this country. One of the high school teachers in Alice, Mr. Larry O'Rear, returned to the University of Texas for further training in science and mathematics. When he returned to Alice, he both offered enriched courses(which I took) and morning enrichment classes in which we covered material beyond that in our textbooks(which I attended). He also recommended me to his teacher at the University of Texas, Dr. H. B. Curtis, when I received a National Merit Scholarship which could be held anywhere. I attended college at the University of Texas which had "integrated" in the 1950's. Integrated must be in quotes because dorms were still segregated, sports were still segregated, most aspects of campus life remained segregated. It grated on black students. We paid the same fees as everyone else, but were denied access to certain facilities that our money supported. We protested to no avail. I decided to major in math because it was one of the things I had enjoyed most in high school and there was no hope of my really understanding physics. I took reading courses with Dr. Curtis and became one of the applied math students. At Texas, you were either third floor(applied) or fourth floor(pure); there was no mixing.I owe a lot of my success in mathematics to Dr. Curtis. I did not arrive at the University as "just another freshman', and I received guidance from him from my entry into the University until I went off to graduate school. I took a number of courses from him, including a real analysis course out of Halmos book as a (third-year) senior. It was while taking Linear Algebra that I met a new black graduate student who was grading for the course, Vivienne Mayes. The real head of the Pure math department was Robert Lee Moore. He was a well known topologist, inventor of a unique teaching method-"the Moore method" which stresses self-learning. One is not allowed to read books. Everything is learned from first principles. The method had been very successful in producing mathematicians and has been much emulated. After I arrived at Texas and learned of his prestige(before I became identified as a third floor student), I thought of taking one of his courses. An older black student, Walker Hunt, told me he had gone to Moore to ask about taking a course with him. Moore told the student that he was welcome to take his course but that he would start with a C and could only go down from there. I have two things to say about this. Moore, his method and his work are highly thought of in the mathematical world. When he died, there was a laudatory article in the Math Monthly, a publication of the Mathematical Association of America. The image of R. L. Moore [see the web page R. L. Moore - racist mathematician exemplified] in my eyes, however, is that of a mathematician who went to a topology lecture given by a student of R. H. Bing. Bing was a student of Moore. The speaker was what we refer to as Moore's mathematical grandson. When Moore discovered that the student was black, he walked out of the lecture. (Parenthetically, let me say one more good thing about Bing. He was a topologist of world-renowned stature and Texas desperately wanted to attract him back from Wisconsin. Word was that Bing had said he would never return to Texas while Moore was there. Moore died and a year or so later Bing returned to Texas. I have a very different image of R. H. Bing.) I was affected by another transition in American society when I was ready to begin graduate school. Rice University was a private university which, according to its Founder's will was for white citizens of Texas. The University had broken the limitation to citizens of Texas years before, and as I prepared to graduate from college in 1963, it had decided to break the part of the will limiting access to whites. Dr. Curtis had his Ph. D. from Rice and he recommended that I attend there. He was going to spend the next year at Rice on sabbatical, which would help ease my transition. I applied, was admitted, and just as I was ready to enter in the summer, the University announced its change of policy. Two alumni sued. As a result I spent a year as a Research Associate, but eventually the University won and I was admitted as a regular student in 1964. I nearly left after my first year when I discovered that I was receiving less money than other students who came in the same year as I did. I applied for and received a NSF graduate fellowship, which I would have been able to use anywhere, but I chose to stay at Rice. I learned this year that I was the first African American to graduate from Rice. I always assumed otherwise because there was an undergraduate who was admitted in 1964 and I assumed she would have graduated first. If I had more time, I would write about how I became perhaps the world's only Hindu-Puerto Rican but it does not directly involve mathematics. Finally, the last transition occurred as I finished graduate school. My advisor, Dr. Jim Douglas, Jr., had left Rice as I was about to finish. I went to Chicago with him, and when I was ready to graduate, he asked where I would like to go. I consulted my wife, and she said, "East". He called a friend at Maryland, and I eventually received an appointment at College Park. (It is hard to believe that it used to be so easy and casual to get an appointment.) I did not know it then, but I was the first African American(actually African anything) to be appointed in the Mathematics Department at College Park. I started my mathematical life working on non-well posed problems. Well posed problems are known to admit good numerical treatments, because you can estimate errors involved with your approximations. Non-well posed problems do not allow such approximations. The problem of determining the temperature at future times, given its current temperature is well-posed. The problem of determining its temperature in the past, given its current temperature is not well-posed. Douglas had a method that allowed you to show that the problem became reasonably well posed if the solutions had certain types of representation in terms of their initial temperatures. I became more interested in the representation of solutions in terms of their initial temperatures, which led me to the study of Besov spaces and harmonic analysis. I have continued to work in harmonic analysis. The adjustment to life in College Park on the non-mathematical side was not easy. The first thing my wife and I saw when we arrived on campus was a large set of "Wallace for President" stickers. I wanted to turn back, but it was too late. I had no idea what I was doing in the classroom, although I had taught a little at Rice. I had little idea of what I was supposed to be doing in research, although a few colleagues like John Benedetto eventually helped. I was promoted though the ranks at Maryland, surviving long enough to become the African American faculty with the longest tenure at College Park. As a reward for this, they made me Chair; frankly, I think I deserved better.