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We prove an interior Lp$L^{p}$-estimate of X-gradient of weak solutions to a class of quasilinear subelliptic equations with VMO coefficients under controllable growth. Here, we use a reverse Hölder inequality and De Giorgi’s iteration to establish the boundedness of their weak solutions. Then a local Lp$L^{p}$-estimate of the X-gradient of the weak solutions is derived by way of the bootstrap argument.

L p $L^{p}$ -Estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth